During a sale, 11 necklaces and 9 bracelets cost $1958. If Gem bought 7 necklaces and 8 bracelets, she would have spent all her money. Each necklace cost $58 more than a bracelet. Find the amount that Gem had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
11 |
9 |
7 |
8 |
| Value |
1 u + 58 |
1 u |
1 u + 58 |
1 u |
| Total value |
11 u + 638 |
9 u |
7 u + 406 |
8 u |
Cost of 1 bracelet = 1 u
Cost of 9 bracelets = 9 u
Cost of 1 necklace = 1 u + 58
Cost of 11 necklaces = 11 x (1 u + 58) = 11 u + 638
Total cost of 9 bracelets and 11 necklaces
= 9 u + 11 u + 638
= 20 u + 638
20 u + 638 = 1958
20 u = 1958 - 638
20 u = 1320
1 u = 1320 ÷ 20 = 66
Cost of 7 necklaces = 7(1 u + 58) = 7 u + 406
Cost of 8 bracelets = 8 u
Amount that Gem had at first
= 7 u + 406 + 8 u
= 15 u + 406
= 15 x 66 + 406
= $1396
Answer(s): $1396
