Bryan and Ivan went shopping with a total amount of $156. They had $130 left after shopping. Bryan's remaining money was 4 times the amount he paid for. Ivan's remaining money was 6 times the amount he had spent.
- How much did Ivan spend?
- How much did Ivan bring along for shopping?
| |
Bryan |
Ivan |
Total |
| Before |
5 u |
7 p |
156 |
| Change |
- 1 u |
- 1 p |
- 26 |
| After |
4 u |
6 p |
130 |
(a)
Amount that Bryan and Ivan spent
= 156 - 130
= $26
Amount that Bryan and Ivan spent
= 1 u + 1 p
1 u + 1 p = 26
1 u = 26 - 1 p --- (1)
Amount that Bryan and Ivan had left
= 4 u + 6 p
4 u + 6 p = 130
4 u = 130 - 6 p --- (2)
Make u the same.
(1)
x 4 4 u = 104 - 4 p --- (3)
(3) = (2)
104 - 4 p = 130 - 6 p
6 p - 4 p = 130 - 104
2 p = 26
1 p = 26 ÷ 2 = 13
Amount that Ivan spent = $13
(b)
Amount that Ivan brought along
= 7 p
= 7 x 13
= $91
Answer(s): (a) $13; (b) $91
