During a sale, 9 rings and 8 bracelets cost $1337. If Cathy bought 7 rings and 10 bracelets, she would have spent all her money. Each ring cost $56 more than a bracelet. Find the amount that Cathy had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
9 |
8 |
7 |
10 |
| Value |
1 u + 56 |
1 u |
1 u + 56 |
1 u |
| Total value |
9 u + 504 |
8 u |
7 u + 392 |
10 u |
Cost of 1 bracelet = 1 u
Cost of 8 bracelets = 8 u
Cost of 1 ring = 1 u + 56
Cost of 9 rings = 9 x (1 u + 56) = 9 u + 504
Total cost of 8 bracelets and 9 rings
= 8 u + 9 u + 504
= 17 u + 504
17 u + 504 = 1337
17 u = 1337 - 504
17 u = 833
1 u = 833 ÷ 17 = 49
Cost of 7 rings = 7(1 u + 56) = 7 u + 392
Cost of 10 bracelets = 10 u
Amount that Cathy had at first
= 7 u + 392 + 10 u
= 17 u + 392
= 17 x 49 + 392
= $1225
Answer(s): $1225
