During a sale, 7 rings and 4 bracelets cost $638. If Risa bought 12 rings and 14 bracelets, she would have spent all her money. Each ring cost $11 more than a bracelet. Find the amount that Risa had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
7 |
4 |
12 |
14 |
| Value |
1 u + 11 |
1 u |
1 u + 11 |
1 u |
| Total value |
7 u + 77 |
4 u |
12 u + 132 |
14 u |
Cost of 1 bracelet = 1 u
Cost of 4 bracelets = 4 u
Cost of 1 ring = 1 u + 11
Cost of 7 rings = 7 x (1 u + 11) = 7 u + 77
Total cost of 4 bracelets and 7 rings
= 4 u + 7 u + 77
= 11 u + 77
11 u + 77 = 638
11 u = 638 - 77
11 u = 561
1 u = 561 ÷ 11 = 51
Cost of 12 rings = 12(1 u + 11) = 12 u + 132
Cost of 14 bracelets = 14 u
Amount that Risa had at first
= 12 u + 132 + 14 u
= 26 u + 132
= 26 x 51 + 132
= $1458
Answer(s): $1458
