Bryan and Adam have a total of $102.
Bryan spends
12 of his money and
Adam spends
16 of his money.
They spend $35 altogether.
- How much does Bryan have at first?
- How much does Adam have in the end?
|
Bryan |
Adam |
Before |
2 u |
6 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
5 p |
(a)
Amount that Bryan has at first = 2 u
Amount that Adam has at first = 6 p
Total amount that they have = 2 u + 6 p = 102 --- (1)
Total amount that they spend = 1 u + 1 p = 35 --- (2)
(2)
x 6 6 u + 6 p = 210 --- (3)
(3) - (1)
(6 u + 6 p) - (2 u + 6 p) = 210 - 102
6 u + 6 p - 2 u - 6 p = 210 - 102
6 u - 2 u + 6 p - 6 p = 108
6 u - 2 u = 108
4 u = 108
1 u = 108 ÷ 4 = 27
Substitute 1 u = 27 into (1).
2 u + 6 p = 102
2 x 27 + 6 p = 102
54 + 6 p = 102
6 p = 102 - 54 = 48
1 p = 48 ÷ 6 = 8
Amount that Bryan has at first
= 2 u
= 2 x 27
= $54
(b)
Amount that Adam has in the end
= 6 p - 1 p
= 5 p
= 5 x 8
= $40
Answer(s): (a) $54; (b) $40