During a sale, 8 rings and 10 necklaces cost $1626. If Fanny bought 12 rings and 15 necklaces, she would have spent all her money. Each ring cost $12 more than a necklace. Find the amount that Fanny had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
8 |
10 |
12 |
15 |
| Value |
1 u + 12 |
1 u |
1 u + 12 |
1 u |
| Total value |
8 u + 96 |
10 u |
12 u + 144 |
15 u |
Cost of 1 necklace = 1 u
Cost of 10 necklaces = 10 u
Cost of 1 ring = 1 u + 12
Cost of 8 rings = 8 x (1 u + 12) = 8 u + 96
Total cost of 10 necklaces and 8 rings
= 10 u + 8 u + 96
= 18 u + 96
18 u + 96 = 1626
18 u = 1626 - 96
18 u = 1530
1 u = 1530 ÷ 18 = 85
Cost of 12 rings = 12(1 u + 12) = 12 u + 144
Cost of 15 necklaces = 15 u
Amount that Fanny had at first
= 12 u + 144 + 15 u
= 27 u + 144
= 27 x 85 + 144
= $2439
Answer(s): $2439
