Ian, Sam and Justin had a total of 52 erasers. The ratio of the number of erasers that Sam had to the number of erasers that Justin had was 8 : 7. After Ian and Sam each gave away half of their erasers, the 3 children had 33 erasers left. How many erasers did Sam and Justin have in the end?
| |
Ian |
Sam |
Justin |
Total |
| Before |
2 p |
8 u |
7 u |
52 |
| Change |
- 1 p |
- 4 u |
|
- 19 |
| After |
1 p |
4 u |
7 u |
33 |
Total number of erasers that Ian and Sam gave away
= 52 - 33
= 19
1 p + 4 u = 19 --- (1)
1 p + 4 u + 7 u = 33
1 p + 11 u = 33 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 4 u) = 33 - 19
11 u - 4 u = 14
7 u = 14
1 u = 14 ÷ 7 = 2
Total number of erasers that Sam and Justin had in the end
= 4 u + 7 u
= 11 u
= 11 x 2
= 22
Answer(s): 22
