Adam and Bryan have a total of $117.
Adam spends
13 of his money and
Bryan spends
16 of his money.
They spend $31 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
3 u |
6 p |
Change |
- 1 u |
- 1 p |
After |
2 u |
5 p |
(a)
Amount that Adam has at first = 3 u
Amount that Bryan has at first = 6 p
Total amount that they have = 3 u + 6 p = 117 --- (1)
Total amount that they spend = 1 u + 1 p = 31 --- (2)
(2)
x 6 6 u + 6 p = 186 --- (3)
(3) - (1)
(6 u + 6 p) - (3 u + 6 p) = 186 - 117
6 u + 6 p - 3 u - 6 p = 186 - 117
6 u - 3 u + 6 p - 6 p = 69
6 u - 3 u = 69
3 u = 69
1 u = 69 ÷ 3 = 23
Substitute 1 u = 23 into (1).
3 u + 6 p = 117
3 x 23 + 6 p = 117
69 + 6 p = 117
6 p = 117 - 69 = 48
1 p = 48 ÷ 6 = 8
Amount that Adam has at first
= 3 u
= 3 x 23
= $69
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 8
= $40
Answer(s): (a) $69; (b) $40