During a sale, 9 bracelets and 8 necklaces cost $2675. If Xandra bought 11 bracelets and 14 necklaces, she would have spent all her money. Each bracelet cost $114 more than a necklace. Find the amount that Xandra had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
9 |
8 |
11 |
14 |
| Value |
1 u + 114 |
1 u |
1 u + 114 |
1 u |
| Total value |
9 u + 1026 |
8 u |
11 u + 1254 |
14 u |
Cost of 1 necklace = 1 u
Cost of 8 necklaces = 8 u
Cost of 1 bracelet = 1 u + 114
Cost of 9 bracelets = 9 x (1 u + 114) = 9 u + 1026
Total cost of 8 necklaces and 9 bracelets
= 8 u + 9 u + 1026
= 17 u + 1026
17 u + 1026 = 2675
17 u = 2675 - 1026
17 u = 1649
1 u = 1649 ÷ 17 = 97
Cost of 11 bracelets = 11(1 u + 114) = 11 u + 1254
Cost of 14 necklaces = 14 u
Amount that Xandra had at first
= 11 u + 1254 + 14 u
= 25 u + 1254
= 25 x 97 + 1254
= $3679
Answer(s): $3679
