Adam and Bryan have a total of $132.
Adam spends
12 of his money and
Bryan spends
16 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 |
6 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
5 p |
(a)
Amount that Adam has at first = 2 u
Amount that Bryan has at first = 6 p
Total amount that they have = 2 u + 6 p = 132 --- (1)
Total amount that they spend = 1 u + 1 p = 42 --- (2)
(2)
x 6 6 u + 6 p = 252 --- (3)
(3) - (1)
(6 u + 6 p) - (2 u + 6 p) = 252 - 132
6 u + 6 p - 2 u - 6 p = 252 - 132
6 u - 2 u + 6 p - 6 p = 120
6 u - 2 u = 120
4 u = 120
1 u = 120 ÷ 4 = 30
Substitute 1 u = 30 into (1).
2 u + 6 p = 132
2 x 30 + 6 p = 132
60 + 6 p = 132
6 p = 132 - 60 = 72
1 p = 72 ÷ 6 = 12
Amount that Adam has at first
= 2 u
= 2 x 30
= $60
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 12
= $60
Answer(s): (a) $60; (b) $60