Age at Event | Worksheet 6/10 - Intermediate-Advanced timed practic...

Question 1

When Austin was born, Hina was 3 years old. The sum of their present ages is 39. Find Austin's age when Austin was half of Hina's age (this will happen 15 years ago).

Let Austin's current age = 18, Hina's current age = 21
Given: When Austin was born (0 years old), Hina was 3 years old.
Therefore, Hina is always 3 years older than Austin.
So 21 = 18 + 3 ✓

Condition: Find t such that Austin's age = ½ of Hina's age
Equation: 18 + t = ½(21 + t)
Multiply both sides by 2: 218 + 2t = 21 + t
Simplify: 218 + 2t - t = 21
218 + t = 21
t = 21 - 218
t = 21 - 36 = -15

At that time, Austin's age = 18 + -15 = 3
Verification: When Austin is 3, Hina is 6 = 6
Check: Is 3 = ½ × 6? ½ × 6 = 3.0 ✓

Note: Mathematically, this always equals the age difference (3) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 2

When Vatsal was born, Krishna was 20 years old. The sum of their present ages is 86. Find Vatsal's age when Vatsal was half of Krishna's age (this will happen 13 years ago).

Let Vatsal's current age = 33, Krishna's current age = 53
Given: When Vatsal was born (0 years old), Krishna was 20 years old.
Therefore, Krishna is always 20 years older than Vatsal.
So 53 = 33 + 20 ✓

Condition: Find t such that Vatsal's age = ½ of Krishna's age
Equation: 33 + t = ½(53 + t)
Multiply both sides by 2: 233 + 2t = 53 + t
Simplify: 233 + 2t - t = 53
233 + t = 53
t = 53 - 233
t = 53 - 66 = -13

At that time, Vatsal's age = 33 + -13 = 20
Verification: When Vatsal is 20, Krishna is 40 = 40
Check: Is 20 = ½ × 40? ½ × 40 = 20.0 ✓

Note: Mathematically, this always equals the age difference (20) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 3

When Emmett was born, Neha was 10 years old. The sum of their present ages is 40. Find Emmett's age when Emmett was half of Neha's age (this will happen 5 years ago).

Let Emmett's current age = 15, Neha's current age = 25
Given: When Emmett was born (0 years old), Neha was 10 years old.
Therefore, Neha is always 10 years older than Emmett.
So 25 = 15 + 10 ✓

Condition: Find t such that Emmett's age = ½ of Neha's age
Equation: 15 + t = ½(25 + t)
Multiply both sides by 2: 215 + 2t = 25 + t
Simplify: 215 + 2t - t = 25
215 + t = 25
t = 25 - 215
t = 25 - 30 = -5

At that time, Emmett's age = 15 + -5 = 10
Verification: When Emmett is 10, Neha is 20 = 20
Check: Is 10 = ½ × 20? ½ × 20 = 10.0 ✓

Note: Mathematically, this always equals the age difference (10) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 4

When Xena was born, Paisley was 18 years old. The sum of their present ages is 80. Find Xena's age when Xena was half of Paisley's age (this will happen 13 years ago).

Let Xena's current age = 31, Paisley's current age = 49
Given: When Xena was born (0 years old), Paisley was 18 years old.
Therefore, Paisley is always 18 years older than Xena.
So 49 = 31 + 18 ✓

Condition: Find t such that Xena's age = ½ of Paisley's age
Equation: 31 + t = ½(49 + t)
Multiply both sides by 2: 231 + 2t = 49 + t
Simplify: 231 + 2t - t = 49
231 + t = 49
t = 49 - 231
t = 49 - 62 = -13

At that time, Xena's age = 31 + -13 = 18
Verification: When Xena is 18, Paisley is 36 = 36
Check: Is 18 = ½ × 36? ½ × 36 = 18.0 ✓

Note: Mathematically, this always equals the age difference (18) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 5

When Karuna was born, Hitesh was 5 years old. The sum of their present ages is 23. Find Karuna's age when Karuna was half of Hitesh's age (this will happen 4 years ago).

Let Karuna's current age = 9, Hitesh's current age = 14
Given: When Karuna was born (0 years old), Hitesh was 5 years old.
Therefore, Hitesh is always 5 years older than Karuna.
So 14 = 9 + 5 ✓

Condition: Find t such that Karuna's age = ½ of Hitesh's age
Equation: 9 + t = ½(14 + t)
Multiply both sides by 2: 29 + 2t = 14 + t
Simplify: 29 + 2t - t = 14
29 + t = 14
t = 14 - 29
t = 14 - 18 = -4

At that time, Karuna's age = 9 + -4 = 5
Verification: When Karuna is 5, Hitesh is 10 = 10
Check: Is 5 = ½ × 10? ½ × 10 = 5.0 ✓

Note: Mathematically, this always equals the age difference (5) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 6

When Shanti was born, Gabriella was 3 years old. The sum of their present ages is 29. Find Shanti's age when Shanti was half of Gabriella's age (this will happen 10 years ago).

Let Shanti's current age = 13, Gabriella's current age = 16
Given: When Shanti was born (0 years old), Gabriella was 3 years old.
Therefore, Gabriella is always 3 years older than Shanti.
So 16 = 13 + 3 ✓

Condition: Find t such that Shanti's age = ½ of Gabriella's age
Equation: 13 + t = ½(16 + t)
Multiply both sides by 2: 213 + 2t = 16 + t
Simplify: 213 + 2t - t = 16
213 + t = 16
t = 16 - 213
t = 16 - 26 = -10

At that time, Shanti's age = 13 + -10 = 3
Verification: When Shanti is 3, Gabriella is 6 = 6
Check: Is 3 = ½ × 6? ½ × 6 = 3.0 ✓

Note: Mathematically, this always equals the age difference (3) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 7

When Robert was born, Tucker was 25 years old. The sum of their present ages is 85. Find Robert's age when Robert was half of Tucker's age (this will happen 5 years ago).

Let Robert's current age = 30, Tucker's current age = 55
Given: When Robert was born (0 years old), Tucker was 25 years old.
Therefore, Tucker is always 25 years older than Robert.
So 55 = 30 + 25 ✓

Condition: Find t such that Robert's age = ½ of Tucker's age
Equation: 30 + t = ½(55 + t)
Multiply both sides by 2: 230 + 2t = 55 + t
Simplify: 230 + 2t - t = 55
230 + t = 55
t = 55 - 230
t = 55 - 60 = -5

At that time, Robert's age = 30 + -5 = 25
Verification: When Robert is 25, Tucker is 50 = 50
Check: Is 25 = ½ × 50? ½ × 50 = 25.0 ✓

Note: Mathematically, this always equals the age difference (25) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 8

When Durga was born, Navya was 21 years old. The sum of their present ages is 81. Find Durga's age when Durga was half of Navya's age (this will happen 9 years ago).

Let Durga's current age = 30, Navya's current age = 51
Given: When Durga was born (0 years old), Navya was 21 years old.
Therefore, Navya is always 21 years older than Durga.
So 51 = 30 + 21 ✓

Condition: Find t such that Durga's age = ½ of Navya's age
Equation: 30 + t = ½(51 + t)
Multiply both sides by 2: 230 + 2t = 51 + t
Simplify: 230 + 2t - t = 51
230 + t = 51
t = 51 - 230
t = 51 - 60 = -9

At that time, Durga's age = 30 + -9 = 21
Verification: When Durga is 21, Navya is 42 = 42
Check: Is 21 = ½ × 42? ½ × 42 = 21.0 ✓

Note: Mathematically, this always equals the age difference (21) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 9

When Mahak was born, Ujjwal was 10 years old. The sum of their present ages is 56. Find Mahak's age when Mahak was half of Ujjwal's age (this will happen 13 years ago).

Let Mahak's current age = 23, Ujjwal's current age = 33
Given: When Mahak was born (0 years old), Ujjwal was 10 years old.
Therefore, Ujjwal is always 10 years older than Mahak.
So 33 = 23 + 10 ✓

Condition: Find t such that Mahak's age = ½ of Ujjwal's age
Equation: 23 + t = ½(33 + t)
Multiply both sides by 2: 223 + 2t = 33 + t
Simplify: 223 + 2t - t = 33
223 + t = 33
t = 33 - 223
t = 33 - 46 = -13

At that time, Mahak's age = 23 + -13 = 10
Verification: When Mahak is 10, Ujjwal is 20 = 20
Check: Is 10 = ½ × 20? ½ × 20 = 10.0 ✓

Note: Mathematically, this always equals the age difference (10) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 10

When Adrian was born, Amit was 15 years old. The sum of their present ages is 57. Find Adrian's age when Adrian was half of Amit's age (this will happen 6 years ago).

Let Adrian's current age = 21, Amit's current age = 36
Given: When Adrian was born (0 years old), Amit was 15 years old.
Therefore, Amit is always 15 years older than Adrian.
So 36 = 21 + 15 ✓

Condition: Find t such that Adrian's age = ½ of Amit's age
Equation: 21 + t = ½(36 + t)
Multiply both sides by 2: 221 + 2t = 36 + t
Simplify: 221 + 2t - t = 36
221 + t = 36
t = 36 - 221
t = 36 - 42 = -6

At that time, Adrian's age = 21 + -6 = 15
Verification: When Adrian is 15, Amit is 30 = 30
Check: Is 15 = ½ × 30? ½ × 30 = 15.0 ✓

Note: Mathematically, this always equals the age difference (15) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 11

When Revathi was born, Uma was 14 years old. The sum of their present ages is 70. Find Revathi's age when Revathi was half of Uma's age (this will happen 14 years ago).

Let Revathi's current age = 28, Uma's current age = 42
Given: When Revathi was born (0 years old), Uma was 14 years old.
Therefore, Uma is always 14 years older than Revathi.
So 42 = 28 + 14 ✓

Condition: Find t such that Revathi's age = ½ of Uma's age
Equation: 28 + t = ½(42 + t)
Multiply both sides by 2: 228 + 2t = 42 + t
Simplify: 228 + 2t - t = 42
228 + t = 42
t = 42 - 228
t = 42 - 56 = -14

At that time, Revathi's age = 28 + -14 = 14
Verification: When Revathi is 14, Uma is 28 = 28
Check: Is 14 = ½ × 28? ½ × 28 = 14.0 ✓

Note: Mathematically, this always equals the age difference (14) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 12

When Prerna was born, Nitin was 10 years old. The sum of their present ages is 58. Find Prerna's age when Prerna was half of Nitin's age (this will happen 14 years ago).

Let Prerna's current age = 24, Nitin's current age = 34
Given: When Prerna was born (0 years old), Nitin was 10 years old.
Therefore, Nitin is always 10 years older than Prerna.
So 34 = 24 + 10 ✓

Condition: Find t such that Prerna's age = ½ of Nitin's age
Equation: 24 + t = ½(34 + t)
Multiply both sides by 2: 224 + 2t = 34 + t
Simplify: 224 + 2t - t = 34
224 + t = 34
t = 34 - 224
t = 34 - 48 = -14

At that time, Prerna's age = 24 + -14 = 10
Verification: When Prerna is 10, Nitin is 20 = 20
Check: Is 10 = ½ × 20? ½ × 20 = 10.0 ✓

Note: Mathematically, this always equals the age difference (10) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 13

When Nandini was born, Hemant was 21 years old. The sum of their present ages is 33. Find Nandini's age when Nandini was half of Hemant's age (this will happen in 15 years).

Let Nandini's current age = 6, Hemant's current age = 27
Given: When Nandini was born (0 years old), Hemant was 21 years old.
Therefore, Hemant is always 21 years older than Nandini.
So 27 = 6 + 21 ✓

Condition: Find t such that Nandini's age = ½ of Hemant's age
Equation: 6 + t = ½(27 + t)
Multiply both sides by 2: 26 + 2t = 27 + t
Simplify: 26 + 2t - t = 27
26 + t = 27
t = 27 - 26
t = 27 - 12 = 15

At that time, Nandini's age = 6 + 15 = 21
Verification: When Nandini is 21, Hemant is 42 = 42
Check: Is 21 = ½ × 42? ½ × 42 = 21.0 ✓

Note: Mathematically, this always equals the age difference (21) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 14

When Nicholas was born, Jai was 9 years old. The sum of their present ages is 41. Find Nicholas's age when Nicholas was half of Jai's age (this will happen 7 years ago).

Let Nicholas's current age = 16, Jai's current age = 25
Given: When Nicholas was born (0 years old), Jai was 9 years old.
Therefore, Jai is always 9 years older than Nicholas.
So 25 = 16 + 9 ✓

Condition: Find t such that Nicholas's age = ½ of Jai's age
Equation: 16 + t = ½(25 + t)
Multiply both sides by 2: 216 + 2t = 25 + t
Simplify: 216 + 2t - t = 25
216 + t = 25
t = 25 - 216
t = 25 - 32 = -7

At that time, Nicholas's age = 16 + -7 = 9
Verification: When Nicholas is 9, Jai is 18 = 18
Check: Is 9 = ½ × 18? ½ × 18 = 9.0 ✓

Note: Mathematically, this always equals the age difference (9) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 15

When Komal was born, Shruti was 19 years old. The sum of their present ages is 67. Find Komal's age when Komal was half of Shruti's age (this will happen 5 years ago).

Let Komal's current age = 24, Shruti's current age = 43
Given: When Komal was born (0 years old), Shruti was 19 years old.
Therefore, Shruti is always 19 years older than Komal.
So 43 = 24 + 19 ✓

Condition: Find t such that Komal's age = ½ of Shruti's age
Equation: 24 + t = ½(43 + t)
Multiply both sides by 2: 224 + 2t = 43 + t
Simplify: 224 + 2t - t = 43
224 + t = 43
t = 43 - 224
t = 43 - 48 = -5

At that time, Komal's age = 24 + -5 = 19
Verification: When Komal is 19, Shruti is 38 = 38
Check: Is 19 = ½ × 38? ½ × 38 = 19.0 ✓

Note: Mathematically, this always equals the age difference (19) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 16

When Om was born, Samantha was 13 years old. The sum of their present ages is 29. Find Om's age when Om was half of Samantha's age (this will happen in 5 years).

Let Om's current age = 8, Samantha's current age = 21
Given: When Om was born (0 years old), Samantha was 13 years old.
Therefore, Samantha is always 13 years older than Om.
So 21 = 8 + 13 ✓

Condition: Find t such that Om's age = ½ of Samantha's age
Equation: 8 + t = ½(21 + t)
Multiply both sides by 2: 28 + 2t = 21 + t
Simplify: 28 + 2t - t = 21
28 + t = 21
t = 21 - 28
t = 21 - 16 = 5

At that time, Om's age = 8 + 5 = 13
Verification: When Om is 13, Samantha is 26 = 26
Check: Is 13 = ½ × 26? ½ × 26 = 13.0 ✓

Note: Mathematically, this always equals the age difference (13) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 17

When Asha was born, Sagar was 4 years old. The sum of their present ages is 18. Find Asha's age when Asha was half of Sagar's age (this will happen 3 years ago).

Let Asha's current age = 7, Sagar's current age = 11
Given: When Asha was born (0 years old), Sagar was 4 years old.
Therefore, Sagar is always 4 years older than Asha.
So 11 = 7 + 4 ✓

Condition: Find t such that Asha's age = ½ of Sagar's age
Equation: 7 + t = ½(11 + t)
Multiply both sides by 2: 27 + 2t = 11 + t
Simplify: 27 + 2t - t = 11
27 + t = 11
t = 11 - 27
t = 11 - 14 = -3

At that time, Asha's age = 7 + -3 = 4
Verification: When Asha is 4, Sagar is 8 = 8
Check: Is 4 = ½ × 8? ½ × 8 = 4.0 ✓

Note: Mathematically, this always equals the age difference (4) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 18

When Harper was born, Pooja was 14 years old. The sum of their present ages is 28. Find Harper's age when Harper was half of Pooja's age (this will happen in 7 years).

Let Harper's current age = 7, Pooja's current age = 21
Given: When Harper was born (0 years old), Pooja was 14 years old.
Therefore, Pooja is always 14 years older than Harper.
So 21 = 7 + 14 ✓

Condition: Find t such that Harper's age = ½ of Pooja's age
Equation: 7 + t = ½(21 + t)
Multiply both sides by 2: 27 + 2t = 21 + t
Simplify: 27 + 2t - t = 21
27 + t = 21
t = 21 - 27
t = 21 - 14 = 7

At that time, Harper's age = 7 + 7 = 14
Verification: When Harper is 14, Pooja is 28 = 28
Check: Is 14 = ½ × 28? ½ × 28 = 14.0 ✓

Note: Mathematically, this always equals the age difference (14) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 19

When Zoey was born, Ezra was 15 years old. The sum of their present ages is 59. Find Zoey's age when Zoey was half of Ezra's age (this will happen 7 years ago).

Let Zoey's current age = 22, Ezra's current age = 37
Given: When Zoey was born (0 years old), Ezra was 15 years old.
Therefore, Ezra is always 15 years older than Zoey.
So 37 = 22 + 15 ✓

Condition: Find t such that Zoey's age = ½ of Ezra's age
Equation: 22 + t = ½(37 + t)
Multiply both sides by 2: 222 + 2t = 37 + t
Simplify: 222 + 2t - t = 37
222 + t = 37
t = 37 - 222
t = 37 - 44 = -7

At that time, Zoey's age = 22 + -7 = 15
Verification: When Zoey is 15, Ezra is 30 = 30
Check: Is 15 = ½ × 30? ½ × 30 = 15.0 ✓

Note: Mathematically, this always equals the age difference (15) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Question 20

When Serenity was born, Isaac was 8 years old. The sum of their present ages is 18. Find Serenity's age when Serenity was half of Isaac's age (this will happen in 3 years).

Let Serenity's current age = 5, Isaac's current age = 13
Given: When Serenity was born (0 years old), Isaac was 8 years old.
Therefore, Isaac is always 8 years older than Serenity.
So 13 = 5 + 8 ✓

Condition: Find t such that Serenity's age = ½ of Isaac's age
Equation: 5 + t = ½(13 + t)
Multiply both sides by 2: 25 + 2t = 13 + t
Simplify: 25 + 2t - t = 13
25 + t = 13
t = 13 - 25
t = 13 - 10 = 3

At that time, Serenity's age = 5 + 3 = 8
Verification: When Serenity is 8, Isaac is 16 = 16
Check: Is 8 = ½ × 16? ½ × 16 = 8.0 ✓

Note: Mathematically, this always equals the age difference (8) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Age at Event: Worksheet 6 - Intermediate-Advanced Practice Age at Event INTERMEDIATE ADVANCED

What you'll learn in this worksheet: