During a sale, 8 necklaces and 5 rings cost $1898. If Rachel bought 7 necklaces and 14 rings, she would have spent all her money. Each necklace cost $104 more than a ring. Find the amount that Rachel had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
8 |
5 |
7 |
14 |
| Value |
1 u + 104 |
1 u |
1 u + 104 |
1 u |
| Total value |
8 u + 832 |
5 u |
7 u + 728 |
14 u |
Cost of 1 ring = 1 u
Cost of 5 rings = 5 u
Cost of 1 necklace = 1 u + 104
Cost of 8 necklaces = 8 x (1 u + 104) = 8 u + 832
Total cost of 5 rings and 8 necklaces
= 5 u + 8 u + 832
= 13 u + 832
13 u + 832 = 1898
13 u = 1898 - 832
13 u = 1066
1 u = 1066 ÷ 13 = 82
Cost of 7 necklaces = 7(1 u + 104) = 7 u + 728
Cost of 14 rings = 14 u
Amount that Rachel had at first
= 7 u + 728 + 14 u
= 21 u + 728
= 21 x 82 + 728
= $2450
Answer(s): $2450
