During a sale, 11 bracelets and 8 rings cost $2720. If Jean bought 9 bracelets and 10 rings, she would have spent all her money. Each bracelet cost $97 more than a ring. Find the amount that Jean had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Rings |
Bracelets |
Rings |
| Number |
11 |
8 |
9 |
10 |
| Value |
1 u + 97 |
1 u |
1 u + 97 |
1 u |
| Total value |
11 u + 1067 |
8 u |
9 u + 873 |
10 u |
Cost of 1 ring = 1 u
Cost of 8 rings = 8 u
Cost of 1 bracelet = 1 u + 97
Cost of 11 bracelets = 11 x (1 u + 97) = 11 u + 1067
Total cost of 8 rings and 11 bracelets
= 8 u + 11 u + 1067
= 19 u + 1067
19 u + 1067 = 2720
19 u = 2720 - 1067
19 u = 1653
1 u = 1653 ÷ 19 = 87
Cost of 9 bracelets = 9(1 u + 97) = 9 u + 873
Cost of 10 rings = 10 u
Amount that Jean had at first
= 9 u + 873 + 10 u
= 19 u + 873
= 19 x 87 + 873
= $2526
Answer(s): $2526
