Adam and Bryan have a total of $84.
Adam spends
12 of his money and
Bryan spends
14 of his money.
They spend $30 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
2 u |
4 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
3 p |
(a)
Amount that Adam has at first = 2 u
Amount that Bryan has at first = 4 p
Total amount that they have = 2 u + 4 p = 84 --- (1)
Total amount that they spend = 1 u + 1 p = 30 --- (2)
(2)
x 4 4 u + 4 p = 120 --- (3)
(3) - (1)
(4 u + 4 p) - (2 u + 4 p) = 120 - 84
4 u + 4 p - 2 u - 4 p = 120 - 84
4 u - 2 u + 4 p - 4 p = 36
4 u - 2 u = 36
2 u = 36
1 u = 36 ÷ 2 = 18
Substitute 1 u = 18 into (1).
2 u + 4 p = 84
2 x 18 + 4 p = 84
36 + 4 p = 84
4 p = 84 - 36 = 48
1 p = 48 ÷ 4 = 12
Amount that Adam has at first
= 2 u
= 2 x 18
= $36
(b)
Amount that Bryan has in the end
= 4 p - 1 p
= 3 p
= 3 x 12
= $36
Answer(s): (a) $36; (b) $36