Adam and Bryan have a total of $298.
Adam spends
14 of his money and
Bryan spends
16 of his money.
They spend $50 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 = 298 --- (1)
Total amount that they spend = 1 u + 1 p = 50 --- (2)
(2)
x 6 6 u + 6 p = 300 --- (3)
(3) - (1)
(6 u + 6 p) - (4 u + 6 p) = 300 - 298
6 u + 6 p - 4 u - 6 p = 300 - 298
6 u - 4 u + 6 p - 6 p = 2
6 u - 4 u = 2
2 u = 2
1 u = 2 ÷ 2 = 1
Substitute 1 u = 1 into (1).
4 u + 6 p = 298
4 x 1 + 6 p = 298
4 + 6 p = 298
6 p = 298 - 4 = 294
1 p = 294 ÷ 6 = 49
Amount that Adam has at first
= 4 u
= 4 x 1
= $4
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 49
= $245
Answer(s): (a) $4; (b) $245