During a sale, 4 necklaces and 6 rings cost $1028. If Emma bought 5 necklaces and 2 rings, she would have spent all her money. Each necklace cost $22 more than a ring. Find the amount that Emma had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
4 |
6 |
5 |
2 |
| Value |
1 u + 22 |
1 u |
1 u + 22 |
1 u |
| Total value |
4 u + 88 |
6 u |
5 u + 110 |
2 u |
Cost of 1 ring = 1 u
Cost of 6 rings = 6 u
Cost of 1 necklace = 1 u + 22
Cost of 4 necklaces = 4 x (1 u + 22) = 4 u + 88
Total cost of 6 rings and 4 necklaces
= 6 u + 4 u + 88
= 10 u + 88
10 u + 88 = 1028
10 u = 1028 - 88
10 u = 940
1 u = 940 ÷ 10 = 94
Cost of 5 necklaces = 5(1 u + 22) = 5 u + 110
Cost of 2 rings = 2 u
Amount that Emma had at first
= 5 u + 110 + 2 u
= 7 u + 110
= 7 x 94 + 110
= $768
Answer(s): $768
