Bryan and Adam have a total of $100.
Bryan spends
12 of his money and
Adam spends
15 of his money.
They spend $23 altogether.
- How much does Bryan have at first?
- How much does Adam have in the end?
|
Bryan |
Adam |
Before |
2 u |
5 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
4 p |
(a)
Amount that Bryan has at first = 2 u
Amount that Adam has at first = 5 p
Total amount that they have = 2 u + 5 p = 100 --- (1)
Total amount that they spend = 1 u + 1 p = 23 --- (2)
(2)
x 5 5 u + 5 p = 115 --- (3)
(3) - (1)
(5 u + 5 p) - (2 u + 5 p) = 115 - 100
5 u + 5 p - 2 u - 5 p = 115 - 100
5 u - 2 u + 5 p - 5 p = 15
5 u - 2 u = 15
3 u = 15
1 u = 15 ÷ 3 = 5
Substitute 1 u = 5 into (1).
2 u + 5 p = 100
2 x 5 + 5 p = 100
10 + 5 p = 100
5 p = 100 - 10 = 90
1 p = 90 ÷ 5 = 18
Amount that Bryan has at first
= 2 u
= 2 x 5
= $10
(b)
Amount that Adam has in the end
= 5 p - 1 p
= 4 p
= 4 x 18
= $72
Answer(s): (a) $10; (b) $72