Bryan and Adam have a total of $122.
Bryan spends
12 of his money and
Adam spends
14 of his money.
They spend $32 altogether.
- How much does Bryan have at first?
- How much does Adam have in the end?
|
Bryan |
Adam |
Before |
2 u |
4 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
3 p |
(a)
Amount that Bryan has at first = 2 u
Amount that Adam has at first = 4 p
Total amount that they have = 2 u + 4 p = 122 --- (1)
Total amount that they spend = 1 u + 1 p = 32 --- (2)
(2)
x 4 4 u + 4 p = 128 --- (3)
(3) - (1)
(4 u + 4 p) - (2 u + 4 p) = 128 - 122
4 u + 4 p - 2 u - 4 p = 128 - 122
4 u - 2 u + 4 p - 4 p = 6
4 u - 2 u = 6
2 u = 6
1 u = 6 ÷ 2 = 3
Substitute 1 u = 3 into (1).
2 u + 4 p = 122
2 x 3 + 4 p = 122
6 + 4 p = 122
4 p = 122 - 6 = 116
1 p = 116 ÷ 4 = 29
Amount that Bryan has at first
= 2 u
= 2 x 3
= $6
(b)
Amount that Adam has in the end
= 4 p - 1 p
= 3 p
= 3 x 29
= $87
Answer(s): (a) $6; (b) $87