During a sale, 12 necklaces and 11 rings cost $1824. If Erika bought 11 necklaces and 2 rings, she would have spent all her money. Each necklace cost $14 more than a ring. Find the amount that Erika had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
12 |
11 |
11 |
2 |
| Value |
1 u + 14 |
1 u |
1 u + 14 |
1 u |
| Total value |
12 u + 168 |
11 u |
11 u + 154 |
2 u |
Cost of 1 ring = 1 u
Cost of 11 rings = 11 u
Cost of 1 necklace = 1 u + 14
Cost of 12 necklaces = 12 x (1 u + 14) = 12 u + 168
Total cost of 11 rings and 12 necklaces
= 11 u + 12 u + 168
= 23 u + 168
23 u + 168 = 1824
23 u = 1824 - 168
23 u = 1656
1 u = 1656 ÷ 23 = 72
Cost of 11 necklaces = 11(1 u + 14) = 11 u + 154
Cost of 2 rings = 2 u
Amount that Erika had at first
= 11 u + 154 + 2 u
= 13 u + 154
= 13 x 72 + 154
= $1090
Answer(s): $1090
