During a sale, 12 necklaces and 10 rings cost $998. If Emily bought 14 necklaces and 10 rings, she would have spent all her money. Each necklace cost $63 more than a ring. Find the amount that Emily had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
12 |
10 |
14 |
10 |
| Value |
1 u + 63 |
1 u |
1 u + 63 |
1 u |
| Total value |
12 u + 756 |
10 u |
14 u + 882 |
10 u |
Cost of 1 ring = 1 u
Cost of 10 rings = 10 u
Cost of 1 necklace = 1 u + 63
Cost of 12 necklaces = 12 x (1 u + 63) = 12 u + 756
Total cost of 10 rings and 12 necklaces
= 10 u + 12 u + 756
= 22 u + 756
22 u + 756 = 998
22 u = 998 - 756
22 u = 242
1 u = 242 ÷ 22 = 11
Cost of 14 necklaces = 14(1 u + 63) = 14 u + 882
Cost of 10 rings = 10 u
Amount that Emily had at first
= 14 u + 882 + 10 u
= 24 u + 882
= 24 x 11 + 882
= $1146
Answer(s): $1146
