During a sale, 6 bracelets and 7 rings cost $1538. If Gabby bought 5 bracelets and 2 rings, she would have spent all her money. Each bracelet cost $96 more than a ring. Find the amount that Gabby had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Rings |
Bracelets |
Rings |
| Number |
6 |
7 |
5 |
2 |
| Value |
1 u + 96 |
1 u |
1 u + 96 |
1 u |
| Total value |
6 u + 576 |
7 u |
5 u + 480 |
2 u |
Cost of 1 ring = 1 u
Cost of 7 rings = 7 u
Cost of 1 bracelet = 1 u + 96
Cost of 6 bracelets = 6 x (1 u + 96) = 6 u + 576
Total cost of 7 rings and 6 bracelets
= 7 u + 6 u + 576
= 13 u + 576
13 u + 576 = 1538
13 u = 1538 - 576
13 u = 962
1 u = 962 ÷ 13 = 74
Cost of 5 bracelets = 5(1 u + 96) = 5 u + 480
Cost of 2 rings = 2 u
Amount that Gabby had at first
= 5 u + 480 + 2 u
= 7 u + 480
= 7 x 74 + 480
= $998
Answer(s): $998
