During a sale, 10 rings and 4 necklaces cost $1366. If Kimberly bought 13 rings and 15 necklaces, she would have spent all her money. Each ring cost $12 more than a necklace. Find the amount that Kimberly had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
10 |
4 |
13 |
15 |
| Value |
1 u + 12 |
1 u |
1 u + 12 |
1 u |
| Total value |
10 u + 120 |
4 u |
13 u + 156 |
15 u |
Cost of 1 necklace = 1 u
Cost of 4 necklaces = 4 u
Cost of 1 ring = 1 u + 12
Cost of 10 rings = 10 x (1 u + 12) = 10 u + 120
Total cost of 4 necklaces and 10 rings
= 4 u + 10 u + 120
= 14 u + 120
14 u + 120 = 1366
14 u = 1366 - 120
14 u = 1246
1 u = 1246 ÷ 14 = 89
Cost of 13 rings = 13(1 u + 12) = 13 u + 156
Cost of 15 necklaces = 15 u
Amount that Kimberly had at first
= 13 u + 156 + 15 u
= 28 u + 156
= 28 x 89 + 156
= $2648
Answer(s): $2648
