Howard's uncle is 7 times as old as him. His uncle will be 31 years old in 3 years' time. In how many years' time will Howard's age be 70% that of his uncle's?
| |
Howard's uncle |
Howard |
Difference |
Before
(now) |
7x1 =
7 u |
1x1 =
1 u |
6x1 =
6 u |
| Change 1 |
+ 3 |
+ 3 |
|
| After 1 |
31 |
|
|
| Change 2 |
+ ? |
+ ? |
|
| After 2 |
10x2 =
20 u |
7x2 =
14 u |
3x2 =
6 u |
70% =
70100 =
710 Howard's uncle : Howard = 10 : 7
The difference in age between Howard's uncle and Howard always remains the same. Make the difference in age between Howard's uncle and Howard the same. LCM of 6 and 3 is 6.
7 u + 3 = 31
7 u = 31 - 3
7 u = 28
1 u = 28 ÷ 7 = 4
Number of years' time when Howard's age will be 70% that of his uncle's
= 20 u - 31
= 20 x 4 - 31
= 80 - 31
= 49
Answer(s): 49
