Adam and Bryan have a total of $76.
Adam spends
13 of his money and
Bryan spends
15 of his money.
They spend $22 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
3 u |
5 p |
Change |
- 1 u |
- 1 p |
After |
2 u |
4 p |
(a)
Amount that Adam has at first = 3 u
Amount that Bryan has at first = 5 p
Total amount that they have = 3 u + 5 p = 76 --- (1)
Total amount that they spend = 1 u + 1 p = 22 --- (2)
(2)
x 5 5 u + 5 p = 110 --- (3)
(3) - (1)
(5 u + 5 p) - (3 u + 5 p) = 110 - 76
5 u + 5 p - 3 u - 5 p = 110 - 76
5 u - 3 u + 5 p - 5 p = 34
5 u - 3 u = 34
2 u = 34
1 u = 34 ÷ 2 = 17
Substitute 1 u = 17 into (1).
3 u + 5 p = 76
3 x 17 + 5 p = 76
51 + 5 p = 76
5 p = 76 - 51 = 25
1 p = 25 ÷ 5 = 5
Amount that Adam has at first
= 3 u
= 3 x 17
= $51
(b)
Amount that Bryan has in the end
= 5 p - 1 p
= 4 p
= 4 x 5
= $20
Answer(s): (a) $51; (b) $20