During a sale, 10 bracelets and 6 rings cost $566. If Olivia bought 7 bracelets and 8 rings, she would have spent all her money. Each bracelet cost $39 more than a ring. Find the amount that Olivia had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Rings |
Bracelets |
Rings |
| Number |
10 |
6 |
7 |
8 |
| Value |
1 u + 39 |
1 u |
1 u + 39 |
1 u |
| Total value |
10 u + 390 |
6 u |
7 u + 273 |
8 u |
Cost of 1 ring = 1 u
Cost of 6 rings = 6 u
Cost of 1 bracelet = 1 u + 39
Cost of 10 bracelets = 10 x (1 u + 39) = 10 u + 390
Total cost of 6 rings and 10 bracelets
= 6 u + 10 u + 390
= 16 u + 390
16 u + 390 = 566
16 u = 566 - 390
16 u = 176
1 u = 176 ÷ 16 = 11
Cost of 7 bracelets = 7(1 u + 39) = 7 u + 273
Cost of 8 rings = 8 u
Amount that Olivia had at first
= 7 u + 273 + 8 u
= 15 u + 273
= 15 x 11 + 273
= $438
Answer(s): $438
