Adam and Bryan have a total of $262.
Adam spends
12 of his money and
Bryan spends
18 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 |
8 p |
Change |
- 1 u |
- 1 p |
After |
1 u |
7 p |
(a)
Amount that Adam has at first = 2 u
Amount that Bryan has at first = 8 p
Total amount that they have = 2 u + 8 p = 262 --- (1)
Total amount that they spend = 1 u + 1 p = 50 --- (2)
(2)
x 8 8 u + 8 p = 400 --- (3)
(3) - (1)
(8 u + 8 p) - (2 u + 8 p) = 400 - 262
8 u + 8 p - 2 u - 8 p = 400 - 262
8 u - 2 u + 8 p - 8 p = 138
8 u - 2 u = 138
6 u = 138
1 u = 138 ÷ 6 = 23
Substitute 1 u = 23 into (1).
2 u + 8 p = 262
2 x 23 + 8 p = 262
46 + 8 p = 262
8 p = 262 - 46 = 216
1 p = 216 ÷ 8 = 27
Amount that Adam has at first
= 2 u
= 2 x 23
= $46
(b)
Amount that Bryan has in the end
= 8 p - 1 p
= 7 p
= 7 x 27
= $189
Answer(s): (a) $46; (b) $189