Adam and Bryan have a total of $169.
Adam spends
13 of his money and
Bryan spends
18 of his money.
They spend $38 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
3 u |
8 p |
Change |
- 1 u |
- 1 p |
After |
2 u |
7 p |
(a)
Amount that Adam has at first = 3 u
Amount that Bryan has at first = 8 p
Total amount that they have = 3 u + 8 p = 169 --- (1)
Total amount that they spend = 1 u + 1 p = 38 --- (2)
(2)
x 8 8 u + 8 p = 304 --- (3)
(3) - (1)
(8 u + 8 p) - (3 u + 8 p) = 304 - 169
8 u + 8 p - 3 u - 8 p = 304 - 169
8 u - 3 u + 8 p - 8 p = 135
8 u - 3 u = 135
5 u = 135
1 u = 135 ÷ 5 = 27
Substitute 1 u = 27 into (1).
3 u + 8 p = 169
3 x 27 + 8 p = 169
81 + 8 p = 169
8 p = 169 - 81 = 88
1 p = 88 ÷ 8 = 11
Amount that Adam has at first
= 3 u
= 3 x 27
= $81
(b)
Amount that Bryan has in the end
= 8 p - 1 p
= 7 p
= 7 x 11
= $77
Answer(s): (a) $81; (b) $77