During a sale, 4 necklaces and 10 rings cost $1060. If Dana bought 13 necklaces and 11 rings, she would have spent all her money. Each necklace cost $41 more than a ring. Find the amount that Dana had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
4 |
10 |
13 |
11 |
| Value |
1 u + 41 |
1 u |
1 u + 41 |
1 u |
| Total value |
4 u + 164 |
10 u |
13 u + 533 |
11 u |
Cost of 1 ring = 1 u
Cost of 10 rings = 10 u
Cost of 1 necklace = 1 u + 41
Cost of 4 necklaces = 4 x (1 u + 41) = 4 u + 164
Total cost of 10 rings and 4 necklaces
= 10 u + 4 u + 164
= 14 u + 164
14 u + 164 = 1060
14 u = 1060 - 164
14 u = 896
1 u = 896 ÷ 14 = 64
Cost of 13 necklaces = 13(1 u + 41) = 13 u + 533
Cost of 11 rings = 11 u
Amount that Dana had at first
= 13 u + 533 + 11 u
= 24 u + 533
= 24 x 64 + 533
= $2069
Answer(s): $2069
