Justin, Rael and Sean had a total of 54 marbles. The ratio of the number of marbles that Rael had to the number of marbles that Sean had was 6 : 5. After Justin and Rael each gave away half of their marbles, the 3 children had 37 marbles left. How many marbles did Rael and Sean have in the end?
| |
Justin |
Rael |
Sean |
Total |
| Before |
2 p |
6 u |
5 u |
54 |
| Change |
- 1 p |
- 3 u |
|
- 17 |
| After |
1 p |
3 u |
5 u |
37 |
Total number of marbles that Justin and Rael gave away
= 54 - 37
= 17
1 p + 3 u = 17 --- (1)
1 p + 3 u + 5 u = 37
1 p + 8 u = 37 --- (2)
(2) - (1)
(1 p + 8 u) - (1 p + 3 u) = 37 - 17
8 u - 3 u = 20
5 u = 20
1 u = 20 ÷ 5 = 4
Total number of marbles that Rael and Sean had in the end
= 3 u + 5 u
= 8 u
= 8 x 4
= 32
Answer(s): 32
