Bryan and Adam have a total of $123.
Bryan spends
13 of his money and
Adam spends
16 of his money.
They spend $33 altogether.
- How much does Bryan have at first?
- How much does Adam have in the end?
|
Bryan |
Adam |
Before |
3 u |
6 p |
Change |
- 1 u |
- 1 p |
After |
2 u |
5 p |
(a)
Amount that Bryan has at first = 3 u
Amount that Adam has at first = 6 p
Total amount that they have = 3 u + 6 p = 123 --- (1)
Total amount that they spend = 1 u + 1 p = 33 --- (2)
(2)
x 6 6 u + 6 p = 198 --- (3)
(3) - (1)
(6 u + 6 p) - (3 u + 6 p) = 198 - 123
6 u + 6 p - 3 u - 6 p = 198 - 123
6 u - 3 u + 6 p - 6 p = 75
6 u - 3 u = 75
3 u = 75
1 u = 75 ÷ 3 = 25
Substitute 1 u = 25 into (1).
3 u + 6 p = 123
3 x 25 + 6 p = 123
75 + 6 p = 123
6 p = 123 - 75 = 48
1 p = 48 ÷ 6 = 8
Amount that Bryan has at first
= 3 u
= 3 x 25
= $75
(b)
Amount that Adam has in the end
= 6 p - 1 p
= 5 p
= 5 x 8
= $40
Answer(s): (a) $75; (b) $40