During a sale, 5 bracelets and 3 necklaces cost $704. If Emma bought 3 bracelets and 8 necklaces, she would have spent all her money. Each bracelet cost $72 more than a necklace. Find the amount that Emma had at first.
|
Case 1 |
Case 2 |
|
Bracelets |
Necklaces |
Bracelets |
Necklaces |
Number |
5 |
3 |
3 |
8 |
Value |
1 u + 72 |
1 u |
1 u + 72 |
1 u |
Total value |
5 u + 360 |
3 u |
3 u + 216 |
8 u |
Cost of 1 necklace = 1 u
Cost of 3 necklaces = 3 u
Cost of 1 bracelet = 1 u + 72
Cost of 5 bracelets = 5 x (1 u + 72) = 5 u + 360
Total cost of 3 necklaces and 5 bracelets
= 3 u + 5 u + 360
= 8 u + 360
8 u + 360 = 704
8 u = 704 - 360
8 u = 344
1 u = 344 ÷ 8 = 43
Cost of 3 bracelets = 3(1 u + 72) = 3 u + 216
Cost of 8 necklaces = 8 u
Amount that Emma had at first
= 3 u + 216 + 8 u
= 11 u + 216
= 11 x 43 + 216
= $689
Answer(s): $689