Adam and Bryan have a total of $270.
Adam spends
14 of his money and
Bryan spends
16 of his money.
They spend $49 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
4 u |
6 p |
Change |
- 1 u |
- 1 p |
After |
3 u |
5 p |
(a)
Amount that Adam has at first = 4 u
Amount that Bryan has at first = 6 p
Total amount that they have = 4 u + 6 p = 270 --- (1)
Total amount that they spend = 1 u + 1 p = 49 --- (2)
(2)
x 6 6 u + 6 p = 294 --- (3)
(3) - (1)
(6 u + 6 p) - (4 u + 6 p) = 294 - 270
6 u + 6 p - 4 u - 6 p = 294 - 270
6 u - 4 u + 6 p - 6 p = 24
6 u - 4 u = 24
2 u = 24
1 u = 24 ÷ 2 = 12
Substitute 1 u = 12 into (1).
4 u + 6 p = 270
4 x 12 + 6 p = 270
48 + 6 p = 270
6 p = 270 - 48 = 222
1 p = 222 ÷ 6 = 37
Amount that Adam has at first
= 4 u
= 4 x 12
= $48
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 37
= $185
Answer(s): (a) $48; (b) $185