David and Sam went shopping with a total amount of $444. They had $370 left after shopping. David's remaining money was 3 times the amount he paid for. Sam's remaining money was 7 times the amount he had spent.
- How much did Sam spend?
- How much did Sam bring along for shopping?
| |
David |
Sam |
Total |
| Before |
4 u |
8 p |
444 |
| Change |
- 1 u |
- 1 p |
- 74 |
| After |
3 u |
7 p |
370 |
(a)
Amount that David and Sam spent
= 444 - 370
= $74
Amount that David and Sam spent
= 1 u + 1 p
1 u + 1 p = 74
1 u = 74 - 1 p --- (1)
Amount that David and Sam had left
= 3 u + 7 p
3 u + 7 p = 370
3 u = 370 - 7 p --- (2)
Make u the same.
(1)
x 3 3 u = 222 - 3 p --- (3)
(3) = (2)
222 - 3 p = 370 - 7 p
7 p - 3 p = 370 - 222
4 p = 148
1 p = 148 ÷ 4 = 37
Amount that Sam spent = $37
(b)
Amount that Sam brought along
= 8 p
= 8 x 37
= $296
Answer(s): (a) $37; (b) $296
