Adam and Bryan have a total of $99.
Adam spends
12 of his money and
Bryan spends
15 of his money.
They spend $42 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
2 u |
5 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
4 p |
(a)
Amount that Adam has at first = 2 u
Amount that Bryan has at first = 5 p
Total amount that they have = 2 u + 5 p = 99 --- (1)
Total amount that they spend = 1 u + 1 p = 42 --- (2)
(2)
x 5 5 u + 5 p = 210 --- (3)
(3) - (1)
(5 u + 5 p) - (2 u + 5 p) = 210 - 99
5 u + 5 p - 2 u - 5 p = 210 - 99
5 u - 2 u + 5 p - 5 p = 111
5 u - 2 u = 111
3 u = 111
1 u = 111 ÷ 3 = 37
Substitute 1 u = 37 into (1).
2 u + 5 p = 99
2 x 37 + 5 p = 99
74 + 5 p = 99
5 p = 99 - 74 = 25
1 p = 25 ÷ 5 = 5
Amount that Adam has at first
= 2 u
= 2 x 37
= $74
(b)
Amount that Bryan has in the end
= 5 p - 1 p
= 4 p
= 4 x 5
= $20
Answer(s): (a) $74; (b) $20