During a sale, 12 necklaces and 4 rings cost $1024. If Tiffany bought 4 necklaces and 12 rings, she would have spent all her money. Each necklace cost $72 more than a ring. Find the amount that Tiffany had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
12 |
4 |
4 |
12 |
| Value |
1 u + 72 |
1 u |
1 u + 72 |
1 u |
| Total value |
12 u + 864 |
4 u |
4 u + 288 |
12 u |
Cost of 1 ring = 1 u
Cost of 4 rings = 4 u
Cost of 1 necklace = 1 u + 72
Cost of 12 necklaces = 12 x (1 u + 72) = 12 u + 864
Total cost of 4 rings and 12 necklaces
= 4 u + 12 u + 864
= 16 u + 864
16 u + 864 = 1024
16 u = 1024 - 864
16 u = 160
1 u = 160 ÷ 16 = 10
Cost of 4 necklaces = 4(1 u + 72) = 4 u + 288
Cost of 12 rings = 12 u
Amount that Tiffany had at first
= 4 u + 288 + 12 u
= 16 u + 288
= 16 x 10 + 288
= $448
Answer(s): $448
