During a sale, 12 necklaces and 4 rings cost $584. If Wendy bought 8 necklaces and 5 rings, she would have spent all her money. Each necklace cost $10 more than a ring. Find the amount that Wendy had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
12 |
4 |
8 |
5 |
| Value |
1 u + 10 |
1 u |
1 u + 10 |
1 u |
| Total value |
12 u + 120 |
4 u |
8 u + 80 |
5 u |
Cost of 1 ring = 1 u
Cost of 4 rings = 4 u
Cost of 1 necklace = 1 u + 10
Cost of 12 necklaces = 12 x (1 u + 10) = 12 u + 120
Total cost of 4 rings and 12 necklaces
= 4 u + 12 u + 120
= 16 u + 120
16 u + 120 = 584
16 u = 584 - 120
16 u = 464
1 u = 464 ÷ 16 = 29
Cost of 8 necklaces = 8(1 u + 10) = 8 u + 80
Cost of 5 rings = 5 u
Amount that Wendy had at first
= 8 u + 80 + 5 u
= 13 u + 80
= 13 x 29 + 80
= $457
Answer(s): $457
