During a sale, 4 necklaces and 3 bracelets cost $338. If Gillian bought 12 necklaces and 11 bracelets, she would have spent all her money. Each necklace cost $53 more than a bracelet. Find the amount that Gillian had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
4 |
3 |
12 |
11 |
| Value |
1 u + 53 |
1 u |
1 u + 53 |
1 u |
| Total value |
4 u + 212 |
3 u |
12 u + 636 |
11 u |
Cost of 1 bracelet = 1 u
Cost of 3 bracelets = 3 u
Cost of 1 necklace = 1 u + 53
Cost of 4 necklaces = 4 x (1 u + 53) = 4 u + 212
Total cost of 3 bracelets and 4 necklaces
= 3 u + 4 u + 212
= 7 u + 212
7 u + 212 = 338
7 u = 338 - 212
7 u = 126
1 u = 126 ÷ 7 = 18
Cost of 12 necklaces = 12(1 u + 53) = 12 u + 636
Cost of 11 bracelets = 11 u
Amount that Gillian had at first
= 12 u + 636 + 11 u
= 23 u + 636
= 23 x 18 + 636
= $1050
Answer(s): $1050
