Adam and Bryan have a total of $287.
Adam spends
13 of his money and
Bryan spends
17 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 |
3 u |
7 p |
Change |
- 1 u |
- 1 p |
After |
2 u |
6 p |
(a)
Amount that Adam has at first = 3 u
Amount that Bryan has at first = 7 p
Total amount that they have = 3 u + 7 p = 287 --- (1)
Total amount that they spend = 1 u + 1 p = 49 --- (2)
(2)
x 7 7 u + 7 p = 343 --- (3)
(3) - (1)
(7 u + 7 p) - (3 u + 7 p) = 343 - 287
7 u + 7 p - 3 u - 7 p = 343 - 287
7 u - 3 u + 7 p - 7 p = 56
7 u - 3 u = 56
4 u = 56
1 u = 56 ÷ 4 = 14
Substitute 1 u = 14 into (1).
3 u + 7 p = 287
3 x 14 + 7 p = 287
42 + 7 p = 287
7 p = 287 - 42 = 245
1 p = 245 ÷ 7 = 35
Amount that Adam has at first
= 3 u
= 3 x 14
= $42
(b)
Amount that Bryan has in the end
= 7 p - 1 p
= 6 p
= 6 x 35
= $210
Answer(s): (a) $42; (b) $210