Ivan and Ryan went shopping with a total amount of $360. They had $300 left after shopping. Ivan's remaining money was 4 times the amount he paid for. Ryan's remaining money was 6 times the amount he had spent.
- How much did Ryan spend?
- How much did Ryan bring along for shopping?
| |
Ivan |
Ryan |
Total |
| Before |
5 u |
7 p |
360 |
| Change |
- 1 u |
- 1 p |
- 60 |
| After |
4 u |
6 p |
300 |
(a)
Amount that Ivan and Ryan spent
= 360 - 300
= $60
Amount that Ivan and Ryan spent
= 1 u + 1 p
1 u + 1 p = 60
1 u = 60 - 1 p --- (1)
Amount that Ivan and Ryan had left
= 4 u + 6 p
4 u + 6 p = 300
4 u = 300 - 6 p --- (2)
Make u the same.
(1)
x 4 4 u = 240 - 4 p --- (3)
(3) = (2)
240 - 4 p = 300 - 6 p
6 p - 4 p = 300 - 240
2 p = 60
1 p = 60 ÷ 2 = 30
Amount that Ryan spent = $30
(b)
Amount that Ryan brought along
= 7 p
= 7 x 30
= $210
Answer(s): (a) $30; (b) $210
