During a sale, 8 necklaces and 5 rings cost $850. If Ivory bought 4 necklaces and 6 rings, she would have spent all her money. Each necklace cost $64 more than a ring. Find the amount that Ivory had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
8 |
5 |
4 |
6 |
| Value |
1 u + 64 |
1 u |
1 u + 64 |
1 u |
| Total value |
8 u + 512 |
5 u |
4 u + 256 |
6 u |
Cost of 1 ring = 1 u
Cost of 5 rings = 5 u
Cost of 1 necklace = 1 u + 64
Cost of 8 necklaces = 8 x (1 u + 64) = 8 u + 512
Total cost of 5 rings and 8 necklaces
= 5 u + 8 u + 512
= 13 u + 512
13 u + 512 = 850
13 u = 850 - 512
13 u = 338
1 u = 338 ÷ 13 = 26
Cost of 4 necklaces = 4(1 u + 64) = 4 u + 256
Cost of 6 rings = 6 u
Amount that Ivory had at first
= 4 u + 256 + 6 u
= 10 u + 256
= 10 x 26 + 256
= $516
Answer(s): $516
