Adam and Bryan have a total of $250.
Adam spends
12 of his money and
Bryan spends
17 of his money.
They spend $50 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
2 u |
7 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
6 p |
(a)
Amount that Adam has at first = 2 u
Amount that Bryan has at first = 7 p
Total amount that they have = 2 u + 7 p = 250 --- (1)
Total amount that they spend = 1 u + 1 p = 50 --- (2)
(2)
x 7 7 u + 7 p = 350 --- (3)
(3) - (1)
(7 u + 7 p) - (2 u + 7 p) = 350 - 250
7 u + 7 p - 2 u - 7 p = 350 - 250
7 u - 2 u + 7 p - 7 p = 100
7 u - 2 u = 100
5 u = 100
1 u = 100 ÷ 5 = 20
Substitute 1 u = 20 into (1).
2 u + 7 p = 250
2 x 20 + 7 p = 250
40 + 7 p = 250
7 p = 250 - 40 = 210
1 p = 210 ÷ 7 = 30
Amount that Adam has at first
= 2 u
= 2 x 20
= $40
(b)
Amount that Bryan has in the end
= 7 p - 1 p
= 6 p
= 6 x 30
= $180
Answer(s): (a) $40; (b) $180