Luke and Tim went shopping with a total amount of $330. They had $270 left after shopping. Luke's remaining money was 3 times the amount he paid for. Tim's remaining money was 6 times the amount he had spent.
- How much did Tim spend?
- How much did Tim bring along for shopping?
| |
Luke |
Tim |
Total |
| Before |
4 u |
7 p |
330 |
| Change |
- 1 u |
- 1 p |
- 60 |
| After |
3 u |
6 p |
270 |
(a)
Amount that Luke and Tim spent
= 330 - 270
= $60
Amount that Luke and Tim spent
= 1 u + 1 p
1 u + 1 p = 60
1 u = 60 - 1 p --- (1)
Amount that Luke and Tim had left
= 3 u + 6 p
3 u + 6 p = 270
3 u = 270 - 6 p --- (2)
Make u the same.
(1)
x 3 3 u = 180 - 3 p --- (3)
(3) = (2)
180 - 3 p = 270 - 6 p
6 p - 3 p = 270 - 180
3 p = 90
1 p = 90 ÷ 3 = 30
Amount that Tim spent = $30
(b)
Amount that Tim brought along
= 7 p
= 7 x 30
= $210
Answer(s): (a) $30; (b) $210
