During a sale, 9 rings and 8 bracelets cost $1710. If Winnie bought 11 rings and 6 bracelets, she would have spent all her money. Each ring cost $20 more than a bracelet. Find the amount that Winnie had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
9 |
8 |
11 |
6 |
| Value |
1 u + 20 |
1 u |
1 u + 20 |
1 u |
| Total value |
9 u + 180 |
8 u |
11 u + 220 |
6 u |
Cost of 1 bracelet = 1 u
Cost of 8 bracelets = 8 u
Cost of 1 ring = 1 u + 20
Cost of 9 rings = 9 x (1 u + 20) = 9 u + 180
Total cost of 8 bracelets and 9 rings
= 8 u + 9 u + 180
= 17 u + 180
17 u + 180 = 1710
17 u = 1710 - 180
17 u = 1530
1 u = 1530 ÷ 17 = 90
Cost of 11 rings = 11(1 u + 20) = 11 u + 220
Cost of 6 bracelets = 6 u
Amount that Winnie had at first
= 11 u + 220 + 6 u
= 17 u + 220
= 17 x 90 + 220
= $1750
Answer(s): $1750
