Adam and Bryan have a total of $284.
Adam spends
14 of his money and
Bryan spends
16 of his money.
They spend $48 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 = 284 --- (1)
Total amount that they spend = 1 u + 1 p = 48 --- (2)
(2)
x 6 6 u + 6 p = 288 --- (3)
(3) - (1)
(6 u + 6 p) - (4 u + 6 p) = 288 - 284
6 u + 6 p - 4 u - 6 p = 288 - 284
6 u - 4 u + 6 p - 6 p = 4
6 u - 4 u = 4
2 u = 4
1 u = 4 ÷ 2 = 2
Substitute 1 u = 2 into (1).
4 u + 6 p = 284
4 x 2 + 6 p = 284
8 + 6 p = 284
6 p = 284 - 8 = 276
1 p = 276 ÷ 6 = 46
Amount that Adam has at first
= 4 u
= 4 x 2
= $8
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 46
= $230
Answer(s): (a) $8; (b) $230