Adam and Bryan have a total of $176.
Adam spends
12 of his money and
Bryan spends
16 of his money.
They spend $34 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 = 176 --- (1)
Total amount that they spend = 1 u + 1 p = 34 --- (2)
(2)
x 6 6 u + 6 p = 204 --- (3)
(3) - (1)
(6 u + 6 p) - (2 u + 6 p) = 204 - 176
6 u + 6 p - 2 u - 6 p = 204 - 176
6 u - 2 u + 6 p - 6 p = 28
6 u - 2 u = 28
4 u = 28
1 u = 28 ÷ 4 = 7
Substitute 1 u = 7 into (1).
2 u + 6 p = 176
2 x 7 + 6 p = 176
14 + 6 p = 176
6 p = 176 - 14 = 162
1 p = 162 ÷ 6 = 27
Amount that Adam has at first
= 2 u
= 2 x 7
= $14
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 27
= $135
Answer(s): (a) $14; (b) $135