During a sale, 3 rings and 5 bracelets cost $623. If Gabby bought 8 rings and 15 bracelets, she would have spent all her money. Each ring cost $77 more than a bracelet. Find the amount that Gabby had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
3 |
5 |
8 |
15 |
| Value |
1 u + 77 |
1 u |
1 u + 77 |
1 u |
| Total value |
3 u + 231 |
5 u |
8 u + 616 |
15 u |
Cost of 1 bracelet = 1 u
Cost of 5 bracelets = 5 u
Cost of 1 ring = 1 u + 77
Cost of 3 rings = 3 x (1 u + 77) = 3 u + 231
Total cost of 5 bracelets and 3 rings
= 5 u + 3 u + 231
= 8 u + 231
8 u + 231 = 623
8 u = 623 - 231
8 u = 392
1 u = 392 ÷ 8 = 49
Cost of 8 rings = 8(1 u + 77) = 8 u + 616
Cost of 15 bracelets = 15 u
Amount that Gabby had at first
= 8 u + 616 + 15 u
= 23 u + 616
= 23 x 49 + 616
= $1743
Answer(s): $1743
