Age at Event: Worksheet 10 - Expert Practice Age at Event EXPERT

Let Sapna's current age = 5, Akshay's current age = 22
Given: When Sapna was born (0 years old), Akshay was 17 years old.
Therefore, Akshay is always 17 years older than Sapna.
So 22 = 5 + 17 ✓

Condition: Find t such that Sapna's age = ½ of Akshay's age
Equation: 5 + t = ½(22 + t)
Multiply both sides by 2: 25 + 2t = 22 + t
Simplify: 25 + 2t - t = 22
25 + t = 22
t = 22 - 25
t = 22 - 10 = 12

At that time, Sapna's age = 5 + 12 = 17
Verification: When Sapna is 17, Akshay is 34 = 34
Check: Is 17 = ½ × 34? ½ × 34 = 17.0 ✓

Note: Mathematically, this always equals the age difference (17) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Let Lisa's current age = 24, Eleanor's current age = 33
Given: When Lisa was born (0 years old), Eleanor was 9 years old.
Therefore, Eleanor is always 9 years older than Lisa.
So 33 = 24 + 9 ✓

Condition: Find t such that Lisa's age = ½ of Eleanor's age
Equation: 24 + t = ½(33 + t)
Multiply both sides by 2: 224 + 2t = 33 + t
Simplify: 224 + 2t - t = 33
224 + t = 33
t = 33 - 224
t = 33 - 48 = -15

At that time, Lisa's age = 24 + -15 = 9
Verification: When Lisa is 9, Eleanor 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

Let Cooper's current age = 20, Theodore's current age = 35
Given: When Cooper was born (0 years old), Theodore was 15 years old.
Therefore, Theodore is always 15 years older than Cooper.
So 35 = 20 + 15 ✓

Condition: Find t such that Cooper's age = ½ of Theodore's age
Equation: 20 + t = ½(35 + t)
Multiply both sides by 2: 220 + 2t = 35 + t
Simplify: 220 + 2t - t = 35
220 + t = 35
t = 35 - 220
t = 35 - 40 = -5

At that time, Cooper's age = 20 + -5 = 15
Verification: When Cooper is 15, Theodore 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

Let Brielle's current age = 5, Vijay's current age = 8
Given: When Brielle was born (0 years old), Vijay was 3 years old.
Therefore, Vijay is always 3 years older than Brielle.
So 8 = 5 + 3 ✓

Condition: Find t such that Brielle's age = ½ of Vijay's age
Equation: 5 + t = ½(8 + t)
Multiply both sides by 2: 25 + 2t = 8 + t
Simplify: 25 + 2t - t = 8
25 + t = 8
t = 8 - 25
t = 8 - 10 = -2

At that time, Brielle's age = 5 + -2 = 3
Verification: When Brielle is 3, Vijay 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

Let Karthik's current age = 17, Dinesh's current age = 32
Given: When Karthik was born (0 years old), Dinesh was 15 years old.
Therefore, Dinesh is always 15 years older than Karthik.
So 32 = 17 + 15 ✓

Condition: Find t such that Karthik's age = ½ of Dinesh's age
Equation: 17 + t = ½(32 + t)
Multiply both sides by 2: 217 + 2t = 32 + t
Simplify: 217 + 2t - t = 32
217 + t = 32
t = 32 - 217
t = 32 - 34 = -2

At that time, Karthik's age = 17 + -2 = 15
Verification: When Karthik is 15, Dinesh 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

Let Amara's current age = 5, Tanya's current age = 20
Given: When Amara was born (0 years old), Tanya was 15 years old.
Therefore, Tanya is always 15 years older than Amara.
So 20 = 5 + 15 ✓

Condition: Find t such that Amara's age = ½ of Tanya's age
Equation: 5 + t = ½(20 + t)
Multiply both sides by 2: 25 + 2t = 20 + t
Simplify: 25 + 2t - t = 20
25 + t = 20
t = 20 - 25
t = 20 - 10 = 10

At that time, Amara's age = 5 + 10 = 15
Verification: When Amara is 15, Tanya 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

Let Indu's current age = 5, Hardik's current age = 20
Given: When Indu was born (0 years old), Hardik was 15 years old.
Therefore, Hardik is always 15 years older than Indu.
So 20 = 5 + 15 ✓

Condition: Find t such that Indu's age = ½ of Hardik's age
Equation: 5 + t = ½(20 + t)
Multiply both sides by 2: 25 + 2t = 20 + t
Simplify: 25 + 2t - t = 20
25 + t = 20
t = 20 - 25
t = 20 - 10 = 10

At that time, Indu's age = 5 + 10 = 15
Verification: When Indu is 15, Hardik 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

Let Ashish's current age = 26, Tripti's current age = 42
Given: When Ashish was born (0 years old), Tripti was 16 years old.
Therefore, Tripti is always 16 years older than Ashish.
So 42 = 26 + 16 ✓

Condition: Find t such that Ashish's age = ½ of Tripti's age
Equation: 26 + t = ½(42 + t)
Multiply both sides by 2: 226 + 2t = 42 + t
Simplify: 226 + 2t - t = 42
226 + t = 42
t = 42 - 226
t = 42 - 52 = -10

At that time, Ashish's age = 26 + -10 = 16
Verification: When Ashish is 16, Tripti is 32 = 32
Check: Is 16 = ½ × 32? ½ × 32 = 16.0 ✓

Note: Mathematically, this always equals the age difference (16) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Let Deepa's current age = 13, Thomas's current age = 23
Given: When Deepa was born (0 years old), Thomas was 10 years old.
Therefore, Thomas is always 10 years older than Deepa.
So 23 = 13 + 10 ✓

Condition: Find t such that Deepa's age = ½ of Thomas's age
Equation: 13 + t = ½(23 + t)
Multiply both sides by 2: 213 + 2t = 23 + t
Simplify: 213 + 2t - t = 23
213 + t = 23
t = 23 - 213
t = 23 - 26 = -3

At that time, Deepa's age = 13 + -3 = 10
Verification: When Deepa is 10, Thomas 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

Let Isabella's current age = 11, Piya's current age = 14
Given: When Isabella was born (0 years old), Piya was 3 years old.
Therefore, Piya is always 3 years older than Isabella.
So 14 = 11 + 3 ✓

Condition: Find t such that Isabella's age = ½ of Piya's age
Equation: 11 + t = ½(14 + t)
Multiply both sides by 2: 211 + 2t = 14 + t
Simplify: 211 + 2t - t = 14
211 + t = 14
t = 14 - 211
t = 14 - 22 = -8

At that time, Isabella's age = 11 + -8 = 3
Verification: When Isabella is 3, Piya 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

Let Jordan's current age = 18, Rajat's current age = 22
Given: When Jordan was born (0 years old), Rajat was 4 years old.
Therefore, Rajat is always 4 years older than Jordan.
So 22 = 18 + 4 ✓

Condition: Find t such that Jordan's age = ½ of Rajat's age
Equation: 18 + t = ½(22 + t)
Multiply both sides by 2: 218 + 2t = 22 + t
Simplify: 218 + 2t - t = 22
218 + t = 22
t = 22 - 218
t = 22 - 36 = -14

At that time, Jordan's age = 18 + -14 = 4
Verification: When Jordan is 4, Rajat 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

Let Dev's current age = 31, Madelyn's current age = 51
Given: When Dev was born (0 years old), Madelyn was 20 years old.
Therefore, Madelyn is always 20 years older than Dev.
So 51 = 31 + 20 ✓

Condition: Find t such that Dev's age = ½ of Madelyn's age
Equation: 31 + t = ½(51 + t)
Multiply both sides by 2: 231 + 2t = 51 + t
Simplify: 231 + 2t - t = 51
231 + t = 51
t = 51 - 231
t = 51 - 62 = -11

At that time, Dev's age = 31 + -11 = 20
Verification: When Dev is 20, Madelyn 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

Let Tushar's current age = 8, Diego's current age = 17
Given: When Tushar was born (0 years old), Diego was 9 years old.
Therefore, Diego is always 9 years older than Tushar.
So 17 = 8 + 9 ✓

Condition: Find t such that Tushar's age = ½ of Diego's age
Equation: 8 + t = ½(17 + t)
Multiply both sides by 2: 28 + 2t = 17 + t
Simplify: 28 + 2t - t = 17
28 + t = 17
t = 17 - 28
t = 17 - 16 = 1

At that time, Tushar's age = 8 + 1 = 9
Verification: When Tushar is 9, Diego 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

Let Angel's current age = 30, Cole's current age = 52
Given: When Angel was born (0 years old), Cole was 22 years old.
Therefore, Cole is always 22 years older than Angel.
So 52 = 30 + 22 ✓

Condition: Find t such that Angel's age = ½ of Cole's age
Equation: 30 + t = ½(52 + t)
Multiply both sides by 2: 230 + 2t = 52 + t
Simplify: 230 + 2t - t = 52
230 + t = 52
t = 52 - 230
t = 52 - 60 = -8

At that time, Angel's age = 30 + -8 = 22
Verification: When Angel is 22, Cole is 44 = 44
Check: Is 22 = ½ × 44? ½ × 44 = 22.0 ✓

Note: Mathematically, this always equals the age difference (22) because:
event_age = current_a + t = current_a + (current_b - 2·current_a) = current_b - current_a = age_diff

Let Adrian's current age = 5, Vedika's current age = 15
Given: When Adrian was born (0 years old), Vedika was 10 years old.
Therefore, Vedika is always 10 years older than Adrian.
So 15 = 5 + 10 ✓

Condition: Find t such that Adrian's age = ½ of Vedika's age
Equation: 5 + t = ½(15 + t)
Multiply both sides by 2: 25 + 2t = 15 + t
Simplify: 25 + 2t - t = 15
25 + t = 15
t = 15 - 25
t = 15 - 10 = 5

At that time, Adrian's age = 5 + 5 = 10
Verification: When Adrian is 10, Vedika 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

Let Tatiana's current age = 28, Silas's current age = 41
Given: When Tatiana was born (0 years old), Silas was 13 years old.
Therefore, Silas is always 13 years older than Tatiana.
So 41 = 28 + 13 ✓

Condition: Find t such that Tatiana's age = ½ of Silas's age
Equation: 28 + t = ½(41 + t)
Multiply both sides by 2: 228 + 2t = 41 + t
Simplify: 228 + 2t - t = 41
228 + t = 41
t = 41 - 228
t = 41 - 56 = -15

At that time, Tatiana's age = 28 + -15 = 13
Verification: When Tatiana is 13, Silas 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

Let Radhika's current age = 5, Priyanka's current age = 9
Given: When Radhika was born (0 years old), Priyanka was 4 years old.
Therefore, Priyanka is always 4 years older than Radhika.
So 9 = 5 + 4 ✓

Condition: Find t such that Radhika's age = ½ of Priyanka's age
Equation: 5 + t = ½(9 + t)
Multiply both sides by 2: 25 + 2t = 9 + t
Simplify: 25 + 2t - t = 9
25 + t = 9
t = 9 - 25
t = 9 - 10 = -1

At that time, Radhika's age = 5 + -1 = 4
Verification: When Radhika is 4, Priyanka 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

Let Sandeep's current age = 9, Urvi's current age = 24
Given: When Sandeep was born (0 years old), Urvi was 15 years old.
Therefore, Urvi is always 15 years older than Sandeep.
So 24 = 9 + 15 ✓

Condition: Find t such that Sandeep's age = ½ of Urvi's age
Equation: 9 + t = ½(24 + t)
Multiply both sides by 2: 29 + 2t = 24 + t
Simplify: 29 + 2t - t = 24
29 + t = 24
t = 24 - 29
t = 24 - 18 = 6

At that time, Sandeep's age = 9 + 6 = 15
Verification: When Sandeep is 15, Urvi 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

Let Addison's current age = 14, Arlo's current age = 35
Given: When Addison was born (0 years old), Arlo was 21 years old.
Therefore, Arlo is always 21 years older than Addison.
So 35 = 14 + 21 ✓

Condition: Find t such that Addison's age = ½ of Arlo's age
Equation: 14 + t = ½(35 + t)
Multiply both sides by 2: 214 + 2t = 35 + t
Simplify: 214 + 2t - t = 35
214 + t = 35
t = 35 - 214
t = 35 - 28 = 7

At that time, Addison's age = 14 + 7 = 21
Verification: When Addison is 21, Arlo 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

Let Kenji's current age = 22, Jai's current age = 47
Given: When Kenji was born (0 years old), Jai was 25 years old.
Therefore, Jai is always 25 years older than Kenji.
So 47 = 22 + 25 ✓

Condition: Find t such that Kenji's age = ½ of Jai's age
Equation: 22 + t = ½(47 + t)
Multiply both sides by 2: 222 + 2t = 47 + t
Simplify: 222 + 2t - t = 47
222 + t = 47
t = 47 - 222
t = 47 - 44 = 3

At that time, Kenji's age = 22 + 3 = 25
Verification: When Kenji is 25, Jai 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