Adam and Bryan have a total of $138.
Adam spends
13 of his money and
Bryan spends
16 of his money.
They spend $36 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
3 u |
6 p |
Change |
- 1 u |
- 1 p |
After |
2 u |
5 p |
(a)
Amount that Adam has at first = 3 u
Amount that Bryan has at first = 6 p
Total amount that they have = 3 u + 6 p = 138 --- (1)
Total amount that they spend = 1 u + 1 p = 36 --- (2)
(2)
x 6 6 u + 6 p = 216 --- (3)
(3) - (1)
(6 u + 6 p) - (3 u + 6 p) = 216 - 138
6 u + 6 p - 3 u - 6 p = 216 - 138
6 u - 3 u + 6 p - 6 p = 78
6 u - 3 u = 78
3 u = 78
1 u = 78 ÷ 3 = 26
Substitute 1 u = 26 into (1).
3 u + 6 p = 138
3 x 26 + 6 p = 138
78 + 6 p = 138
6 p = 138 - 78 = 60
1 p = 60 ÷ 6 = 10
Amount that Adam has at first
= 3 u
= 3 x 26
= $78
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 10
= $50
Answer(s): (a) $78; (b) $50