During a sale, 6 rings and 11 bracelets cost $826. If Shannon bought 8 rings and 15 bracelets, she would have spent all her money. Each ring cost $13 more than a bracelet. Find the amount that Shannon had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
6 |
11 |
8 |
15 |
| Value |
1 u + 13 |
1 u |
1 u + 13 |
1 u |
| Total value |
6 u + 78 |
11 u |
8 u + 104 |
15 u |
Cost of 1 bracelet = 1 u
Cost of 11 bracelets = 11 u
Cost of 1 ring = 1 u + 13
Cost of 6 rings = 6 x (1 u + 13) = 6 u + 78
Total cost of 11 bracelets and 6 rings
= 11 u + 6 u + 78
= 17 u + 78
17 u + 78 = 826
17 u = 826 - 78
17 u = 748
1 u = 748 ÷ 17 = 44
Cost of 8 rings = 8(1 u + 13) = 8 u + 104
Cost of 15 bracelets = 15 u
Amount that Shannon had at first
= 8 u + 104 + 15 u
= 23 u + 104
= 23 x 44 + 104
= $1116
Answer(s): $1116
