Rael had $429 more money than Fred at first. After Rael spent
23 of his money to buy a jacket and Fred spent
15 of his money to buy a sweater, they had a total of $466 left. How much more did the jacket cost than the sweater?
|
Rael |
Fred |
Comparing Rael and Fred at first |
429 more |
|
Before |
3x5 |
429 |
5x3 |
Change |
- 2x5 |
- 286 |
- 1x3 |
After |
1x5 |
143 |
4x3 |
|
Rael |
Fred |
Before |
15 u + 429 |
15 u |
Change |
- 10 u - 286 |
- 3 u |
After |
5 u + 143 |
12 u |
LCM of 3 and 5 = 15
23 x 429 = 286
429 - 286 = 143
Total amount that Rael and Fred had in the end
= 5 u + 143 + 12 u
= 17 u + 143
17 u + 143 = 466
17 u = 466 - 143
17 u = 323
1 u = 323 ÷ 17 = 19
Amount paid more for the jacket than the sweater
= (10 u + 286) - 3 u
= 10 u - 3 u + 286
= 7 u + 286
= (7 x 19) + 286
= 133 + 286
= $419
Answer: $419