During a sale, 8 bracelets and 5 necklaces cost $1163. If Xandra bought 12 bracelets and 3 necklaces, she would have spent all her money. Each bracelet cost $108 more than a necklace. Find the amount that Xandra had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
8 |
5 |
12 |
3 |
| Value |
1 u + 108 |
1 u |
1 u + 108 |
1 u |
| Total value |
8 u + 864 |
5 u |
12 u + 1296 |
3 u |
Cost of 1 necklace = 1 u
Cost of 5 necklaces = 5 u
Cost of 1 bracelet = 1 u + 108
Cost of 8 bracelets = 8 x (1 u + 108) = 8 u + 864
Total cost of 5 necklaces and 8 bracelets
= 5 u + 8 u + 864
= 13 u + 864
13 u + 864 = 1163
13 u = 1163 - 864
13 u = 299
1 u = 299 ÷ 13 = 23
Cost of 12 bracelets = 12(1 u + 108) = 12 u + 1296
Cost of 3 necklaces = 3 u
Amount that Xandra had at first
= 12 u + 1296 + 3 u
= 15 u + 1296
= 15 x 23 + 1296
= $1641
Answer(s): $1641
