During a sale, 8 necklaces and 3 rings cost $1144. If Esther bought 12 necklaces and 11 rings, she would have spent all her money. Each necklace cost $110 more than a ring. Find the amount that Esther had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
8 |
3 |
12 |
11 |
| Value |
1 u + 110 |
1 u |
1 u + 110 |
1 u |
| Total value |
8 u + 880 |
3 u |
12 u + 1320 |
11 u |
Cost of 1 ring = 1 u
Cost of 3 rings = 3 u
Cost of 1 necklace = 1 u + 110
Cost of 8 necklaces = 8 x (1 u + 110) = 8 u + 880
Total cost of 3 rings and 8 necklaces
= 3 u + 8 u + 880
= 11 u + 880
11 u + 880 = 1144
11 u = 1144 - 880
11 u = 264
1 u = 264 ÷ 11 = 24
Cost of 12 necklaces = 12(1 u + 110) = 12 u + 1320
Cost of 11 rings = 11 u
Amount that Esther had at first
= 12 u + 1320 + 11 u
= 23 u + 1320
= 23 x 24 + 1320
= $1872
Answer(s): $1872
