During a sale, 5 rings and 4 necklaces cost $1459. If Tiffany bought 10 rings and 12 necklaces, she would have spent all her money. Each ring cost $137 more than a necklace. Find the amount that Tiffany had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
5 |
4 |
10 |
12 |
| Value |
1 u + 137 |
1 u |
1 u + 137 |
1 u |
| Total value |
5 u + 685 |
4 u |
10 u + 1370 |
12 u |
Cost of 1 necklace = 1 u
Cost of 4 necklaces = 4 u
Cost of 1 ring = 1 u + 137
Cost of 5 rings = 5 x (1 u + 137) = 5 u + 685
Total cost of 4 necklaces and 5 rings
= 4 u + 5 u + 685
= 9 u + 685
9 u + 685 = 1459
9 u = 1459 - 685
9 u = 774
1 u = 774 ÷ 9 = 86
Cost of 10 rings = 10(1 u + 137) = 10 u + 1370
Cost of 12 necklaces = 12 u
Amount that Tiffany had at first
= 10 u + 1370 + 12 u
= 22 u + 1370
= 22 x 86 + 1370
= $3262
Answer(s): $3262
