During a sale, 8 necklaces and 6 bracelets cost $1038. If Anna bought 6 necklaces and 14 bracelets, she would have spent all her money. Each necklace cost $107 more than a bracelet. Find the amount that Anna had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
8 |
6 |
6 |
14 |
| Value |
1 u + 107 |
1 u |
1 u + 107 |
1 u |
| Total value |
8 u + 856 |
6 u |
6 u + 642 |
14 u |
Cost of 1 bracelet = 1 u
Cost of 6 bracelets = 6 u
Cost of 1 necklace = 1 u + 107
Cost of 8 necklaces = 8 x (1 u + 107) = 8 u + 856
Total cost of 6 bracelets and 8 necklaces
= 6 u + 8 u + 856
= 14 u + 856
14 u + 856 = 1038
14 u = 1038 - 856
14 u = 182
1 u = 182 ÷ 14 = 13
Cost of 6 necklaces = 6(1 u + 107) = 6 u + 642
Cost of 14 bracelets = 14 u
Amount that Anna had at first
= 6 u + 642 + 14 u
= 20 u + 642
= 20 x 13 + 642
= $902
Answer(s): $902
