During a sale, 11 bracelets and 10 rings cost $2172. If Barbara bought 12 bracelets and 14 rings, she would have spent all her money. Each bracelet cost $144 more than a ring. Find the amount that Barbara had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Rings |
Bracelets |
Rings |
| Number |
11 |
10 |
12 |
14 |
| Value |
1 u + 144 |
1 u |
1 u + 144 |
1 u |
| Total value |
11 u + 1584 |
10 u |
12 u + 1728 |
14 u |
Cost of 1 ring = 1 u
Cost of 10 rings = 10 u
Cost of 1 bracelet = 1 u + 144
Cost of 11 bracelets = 11 x (1 u + 144) = 11 u + 1584
Total cost of 10 rings and 11 bracelets
= 10 u + 11 u + 1584
= 21 u + 1584
21 u + 1584 = 2172
21 u = 2172 - 1584
21 u = 588
1 u = 588 ÷ 21 = 28
Cost of 12 bracelets = 12(1 u + 144) = 12 u + 1728
Cost of 14 rings = 14 u
Amount that Barbara had at first
= 12 u + 1728 + 14 u
= 26 u + 1728
= 26 x 28 + 1728
= $2456
Answer(s): $2456
