Adam and Bryan have a total of $78.
Adam spends
13 of his money and
Bryan spends
17 of his money.
They spend $14 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 = 78 --- (1)
Total amount that they spend = 1 u + 1 p = 14 --- (2)
(2)
x 7 7 u + 7 p = 98 --- (3)
(3) - (1)
(7 u + 7 p) - (3 u + 7 p) = 98 - 78
7 u + 7 p - 3 u - 7 p = 98 - 78
7 u - 3 u + 7 p - 7 p = 20
7 u - 3 u = 20
4 u = 20
1 u = 20 ÷ 4 = 5
Substitute 1 u = 5 into (1).
3 u + 7 p = 78
3 x 5 + 7 p = 78
15 + 7 p = 78
7 p = 78 - 15 = 63
1 p = 63 ÷ 7 = 9
Amount that Adam has at first
= 3 u
= 3 x 5
= $15
(b)
Amount that Bryan has in the end
= 7 p - 1 p
= 6 p
= 6 x 9
= $54
Answer(s): (a) $15; (b) $54