During a sale, 8 necklaces and 10 bracelets cost $1696. If Gillian bought 5 necklaces and 8 bracelets, she would have spent all her money. Each necklace cost $50 more than a bracelet. Find the amount that Gillian had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
8 |
10 |
5 |
8 |
| Value |
1 u + 50 |
1 u |
1 u + 50 |
1 u |
| Total value |
8 u + 400 |
10 u |
5 u + 250 |
8 u |
Cost of 1 bracelet = 1 u
Cost of 10 bracelets = 10 u
Cost of 1 necklace = 1 u + 50
Cost of 8 necklaces = 8 x (1 u + 50) = 8 u + 400
Total cost of 10 bracelets and 8 necklaces
= 10 u + 8 u + 400
= 18 u + 400
18 u + 400 = 1696
18 u = 1696 - 400
18 u = 1296
1 u = 1296 ÷ 18 = 72
Cost of 5 necklaces = 5(1 u + 50) = 5 u + 250
Cost of 8 bracelets = 8 u
Amount that Gillian had at first
= 5 u + 250 + 8 u
= 13 u + 250
= 13 x 72 + 250
= $1186
Answer(s): $1186
