Adam and Bryan have a total of $183.
Adam spends
12 of his money and
Bryan spends
17 of his money.
They spend $34 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 = 183 --- (1)
Total amount that they spend = 1 u + 1 p = 34 --- (2)
(2)
x 7 7 u + 7 p = 238 --- (3)
(3) - (1)
(7 u + 7 p) - (2 u + 7 p) = 238 - 183
7 u + 7 p - 2 u - 7 p = 238 - 183
7 u - 2 u + 7 p - 7 p = 55
7 u - 2 u = 55
5 u = 55
1 u = 55 ÷ 5 = 11
Substitute 1 u = 11 into (1).
2 u + 7 p = 183
2 x 11 + 7 p = 183
22 + 7 p = 183
7 p = 183 - 22 = 161
1 p = 161 ÷ 7 = 23
Amount that Adam has at first
= 2 u
= 2 x 11
= $22
(b)
Amount that Bryan has in the end
= 7 p - 1 p
= 6 p
= 6 x 23
= $138
Answer(s): (a) $22; (b) $138