During a sale, 12 bracelets and 4 necklaces cost $1140. If Gillian bought 8 bracelets and 4 necklaces, she would have spent all her money. Each bracelet cost $31 more than a necklace. Find the amount that Gillian had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
12 |
4 |
8 |
4 |
| Value |
1 u + 31 |
1 u |
1 u + 31 |
1 u |
| Total value |
12 u + 372 |
4 u |
8 u + 248 |
4 u |
Cost of 1 necklace = 1 u
Cost of 4 necklaces = 4 u
Cost of 1 bracelet = 1 u + 31
Cost of 12 bracelets = 12 x (1 u + 31) = 12 u + 372
Total cost of 4 necklaces and 12 bracelets
= 4 u + 12 u + 372
= 16 u + 372
16 u + 372 = 1140
16 u = 1140 - 372
16 u = 768
1 u = 768 ÷ 16 = 48
Cost of 8 bracelets = 8(1 u + 31) = 8 u + 248
Cost of 4 necklaces = 4 u
Amount that Gillian had at first
= 8 u + 248 + 4 u
= 12 u + 248
= 12 x 48 + 248
= $824
Answer(s): $824
