During a sale, 11 rings and 5 necklaces cost $1292. If Mary bought 10 rings and 2 necklaces, she would have spent all her money. Each ring cost $68 more than a necklace. Find the amount that Mary had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
11 |
5 |
10 |
2 |
| Value |
1 u + 68 |
1 u |
1 u + 68 |
1 u |
| Total value |
11 u + 748 |
5 u |
10 u + 680 |
2 u |
Cost of 1 necklace = 1 u
Cost of 5 necklaces = 5 u
Cost of 1 ring = 1 u + 68
Cost of 11 rings = 11 x (1 u + 68) = 11 u + 748
Total cost of 5 necklaces and 11 rings
= 5 u + 11 u + 748
= 16 u + 748
16 u + 748 = 1292
16 u = 1292 - 748
16 u = 544
1 u = 544 ÷ 16 = 34
Cost of 10 rings = 10(1 u + 68) = 10 u + 680
Cost of 2 necklaces = 2 u
Amount that Mary had at first
= 10 u + 680 + 2 u
= 12 u + 680
= 12 x 34 + 680
= $1088
Answer(s): $1088
