Adam and Bryan have a total of $162.
Adam spends
12 of his money and
Bryan spends
17 of his money.
They spend $46 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 = 162 --- (1)
Total amount that they spend = 1 u + 1 p = 46 --- (2)
(2)
x 7 7 u + 7 p = 322 --- (3)
(3) - (1)
(7 u + 7 p) - (2 u + 7 p) = 322 - 162
7 u + 7 p - 2 u - 7 p = 322 - 162
7 u - 2 u + 7 p - 7 p = 160
7 u - 2 u = 160
5 u = 160
1 u = 160 ÷ 5 = 32
Substitute 1 u = 32 into (1).
2 u + 7 p = 162
2 x 32 + 7 p = 162
64 + 7 p = 162
7 p = 162 - 64 = 98
1 p = 98 ÷ 7 = 14
Amount that Adam has at first
= 2 u
= 2 x 32
= $64
(b)
Amount that Bryan has in the end
= 7 p - 1 p
= 6 p
= 6 x 14
= $84
Answer(s): (a) $64; (b) $84