Mark, Brandon and Xavier had a total of 138 marbles. The ratio of the number of marbles that Brandon had to the number of marbles that Xavier had was 6 : 5. After Mark and Brandon each gave away half of their marbles, the 3 children had 99 marbles left. How many marbles did Brandon and Xavier have at first?
| |
Mark |
Brandon |
Xavier |
Total |
| Before |
2 p |
6 u |
5 u |
138 |
| Change |
- 1 p |
- 3 u |
|
- 39 |
| After |
1 p |
3 u |
5 u |
99 |
Total number of marbles that Mark and Brandon gave away
= 138 - 99
= 39
1 p + 3 u = 39 --- (1)
1 p + 3 u + 5 u = 99
1 p + 8 u = 99 --- (2)
(2) - (1)
(1 p + 8 u) - (1 p + 3 u) = 99 - 39
8 u - 3 u = 60
5 u = 60
1 u = 60 ÷ 5 = 12
Total number of marbles that Brandon and Xavier had at first
= 6 u + 5 u
= 11 u
= 11 x 12
= 132
Answer(s): 132
