During a sale, 10 bracelets and 12 rings cost $2282. If Kathy bought 12 bracelets and 10 rings, she would have spent all her money. Each bracelet cost $50 more than a ring. Find the amount that Kathy had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Rings |
Bracelets |
Rings |
| Number |
10 |
12 |
12 |
10 |
| Value |
1 u + 50 |
1 u |
1 u + 50 |
1 u |
| Total value |
10 u + 500 |
12 u |
12 u + 600 |
10 u |
Cost of 1 ring = 1 u
Cost of 12 rings = 12 u
Cost of 1 bracelet = 1 u + 50
Cost of 10 bracelets = 10 x (1 u + 50) = 10 u + 500
Total cost of 12 rings and 10 bracelets
= 12 u + 10 u + 500
= 22 u + 500
22 u + 500 = 2282
22 u = 2282 - 500
22 u = 1782
1 u = 1782 ÷ 22 = 81
Cost of 12 bracelets = 12(1 u + 50) = 12 u + 600
Cost of 10 rings = 10 u
Amount that Kathy had at first
= 12 u + 600 + 10 u
= 22 u + 600
= 22 x 81 + 600
= $2382
Answer(s): $2382
