During a sale, 6 bracelets and 5 rings cost $1591. If Rachel bought 4 bracelets and 2 rings, she would have spent all her money. Each bracelet cost $124 more than a ring. Find the amount that Rachel had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Rings |
Bracelets |
Rings |
| Number |
6 |
5 |
4 |
2 |
| Value |
1 u + 124 |
1 u |
1 u + 124 |
1 u |
| Total value |
6 u + 744 |
5 u |
4 u + 496 |
2 u |
Cost of 1 ring = 1 u
Cost of 5 rings = 5 u
Cost of 1 bracelet = 1 u + 124
Cost of 6 bracelets = 6 x (1 u + 124) = 6 u + 744
Total cost of 5 rings and 6 bracelets
= 5 u + 6 u + 744
= 11 u + 744
11 u + 744 = 1591
11 u = 1591 - 744
11 u = 847
1 u = 847 ÷ 11 = 77
Cost of 4 bracelets = 4(1 u + 124) = 4 u + 496
Cost of 2 rings = 2 u
Amount that Rachel had at first
= 4 u + 496 + 2 u
= 6 u + 496
= 6 x 77 + 496
= $958
Answer(s): $958
