During a sale, 11 necklaces and 6 rings cost $2547. If Emily bought 7 necklaces and 2 rings, she would have spent all her money. Each necklace cost $145 more than a ring. Find the amount that Emily had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
11 |
6 |
7 |
2 |
| Value |
1 u + 145 |
1 u |
1 u + 145 |
1 u |
| Total value |
11 u + 1595 |
6 u |
7 u + 1015 |
2 u |
Cost of 1 ring = 1 u
Cost of 6 rings = 6 u
Cost of 1 necklace = 1 u + 145
Cost of 11 necklaces = 11 x (1 u + 145) = 11 u + 1595
Total cost of 6 rings and 11 necklaces
= 6 u + 11 u + 1595
= 17 u + 1595
17 u + 1595 = 2547
17 u = 2547 - 1595
17 u = 952
1 u = 952 ÷ 17 = 56
Cost of 7 necklaces = 7(1 u + 145) = 7 u + 1015
Cost of 2 rings = 2 u
Amount that Emily had at first
= 7 u + 1015 + 2 u
= 9 u + 1015
= 9 x 56 + 1015
= $1519
Answer(s): $1519
