Gem will be 99 years old in 15 years' time. Now, Esther's age is 56 of Gem's age. What was Esther's age when she was 3 years more than 75% of Gem's age?
| |
Esther |
Gem |
Difference |
| Before |
3 p + 3 |
4 p |
1 p - 3 |
| Change 1 |
+ ? |
+ ? |
|
| After 1 (Now) |
5 u |
6 u |
1 u |
| Change 2 |
+ 15 |
+ 15 |
|
| After |
5 u + 15 |
99 |
|
Gem's age in 15 years' time = 6 u + 15
6 u + 15 = 99
6 u = 99 - 15
6 u = 84
1 u = 84 ÷ 6 = 14
Difference between Gem's age and Esther's age
= 1 u
= 14
75% =
75100 =
34 Difference in Gem's age and Esther's age at first
= 4 p - (3 p + 3)
= 1 p - 3
The difference in age between Gem and Esther remains unchanged.
1 p - 3 = 14
1 p = 14 + 3 = 17
Esther's age when she was 3 years more than 75% of Gem's age
= 3 p + 3
= 3 x 17 + 3
= 51 + 3
= 54
Answer(s): 54
