During a sale, 3 bracelets and 8 rings cost $1072. If Gabby bought 14 bracelets and 12 rings, she would have spent all her money. Each bracelet cost $53 more than a ring. Find the amount that Gabby had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Rings |
Bracelets |
Rings |
| Number |
3 |
8 |
14 |
12 |
| Value |
1 u + 53 |
1 u |
1 u + 53 |
1 u |
| Total value |
3 u + 159 |
8 u |
14 u + 742 |
12 u |
Cost of 1 ring = 1 u
Cost of 8 rings = 8 u
Cost of 1 bracelet = 1 u + 53
Cost of 3 bracelets = 3 x (1 u + 53) = 3 u + 159
Total cost of 8 rings and 3 bracelets
= 8 u + 3 u + 159
= 11 u + 159
11 u + 159 = 1072
11 u = 1072 - 159
11 u = 913
1 u = 913 ÷ 11 = 83
Cost of 14 bracelets = 14(1 u + 53) = 14 u + 742
Cost of 12 rings = 12 u
Amount that Gabby had at first
= 14 u + 742 + 12 u
= 26 u + 742
= 26 x 83 + 742
= $2900
Answer(s): $2900
