Jane will be 84 years old in 18 years' time. Now, Gem's age is 56 of Jane's age. What was Gem's age when she was 5 years more than 75% of Jane's age?
| |
Gem |
Jane |
Difference |
| Before |
3 p + 5 |
4 p |
1 p - 5 |
| Change 1 |
+ ? |
+ ? |
|
| After 1 (Now) |
5 u |
6 u |
1 u |
| Change 2 |
+ 18 |
+ 18 |
|
| After |
5 u + 18 |
84 |
|
Jane's age in 18 years' time = 6 u + 18
6 u + 18 = 84
6 u = 84 - 18
6 u = 66
1 u = 66 ÷ 6 = 11
Difference between Jane's age and Gem's age
= 1 u
= 11
75% =
75100 =
34 Difference in Jane's age and Gem's age at first
= 4 p - (3 p + 5)
= 1 p - 5
The difference in age between Jane and Gem remains unchanged.
1 p - 5 = 11
1 p = 11 + 5 = 16
Gem's age when she was 5 years more than 75% of Jane's age
= 3 p + 5
= 3 x 16 + 5
= 48 + 5
= 53
Answer(s): 53
