Adam and Bryan have a total of $90.
Adam spends
12 of his money and
Bryan spends
18 of his money.
They spend $39 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
2 u |
8 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
7 p |
(a)
Amount that Adam has at first = 2 u
Amount that Bryan has at first = 8 p
Total amount that they have = 2 u + 8 p = 90 --- (1)
Total amount that they spend = 1 u + 1 p = 39 --- (2)
(2)
x 8 8 u + 8 p = 312 --- (3)
(3) - (1)
(8 u + 8 p) - (2 u + 8 p) = 312 - 90
8 u + 8 p - 2 u - 8 p = 312 - 90
8 u - 2 u + 8 p - 8 p = 222
8 u - 2 u = 222
6 u = 222
1 u = 222 ÷ 6 = 37
Substitute 1 u = 37 into (1).
2 u + 8 p = 90
2 x 37 + 8 p = 90
74 + 8 p = 90
8 p = 90 - 74 = 16
1 p = 16 ÷ 8 = 2
Amount that Adam has at first
= 2 u
= 2 x 37
= $74
(b)
Amount that Bryan has in the end
= 8 p - 1 p
= 7 p
= 7 x 2
= $14
Answer(s): (a) $74; (b) $14