Daniel and Seth went shopping with a total amount of $406. They had $348 left after shopping. Daniel's remaining money was 5 times the amount he paid for. Seth's remaining money was 7 times the amount he had spent.
- How much did Seth spend?
- How much did Seth bring along for shopping?
|
Daniel |
Seth |
Total |
Before |
6 u |
8 p |
406 |
Change |
- 1 u |
- 1 p |
- 58 |
After |
5 u |
7 p |
348 |
(a)
Amount that Daniel and Seth spent
= 406 - 348
= $58
Amount that Daniel and Seth spent
= 1 u + 1 p
1 u + 1 p = 58
1 u = 58 - 1 p --- (1)
Amount that Daniel and Seth had left
= 5 u + 7 p
5 u + 7 p = 348
5 u = 348 - 7 p --- (2)
Make u the same.
(1)
x 5 5 u = 290 - 5 p --- (3)
(3) = (2)
290 - 5 p = 348 - 7 p
7 p - 5 p = 348 - 290
2 p = 58
1 p = 58 ÷ 2 = 29
Amount that Seth spent = $29
(b)
Amount that Seth brought along
= 8 p
= 8 x 29
= $232
Answer(s): (a) $29; (b) $232