During a sale, 12 rings and 3 necklaces cost $1737. If Jean bought 13 rings and 8 necklaces, she would have spent all her money. Each ring cost $41 more than a necklace. Find the amount that Jean had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
12 |
3 |
13 |
8 |
| Value |
1 u + 41 |
1 u |
1 u + 41 |
1 u |
| Total value |
12 u + 492 |
3 u |
13 u + 533 |
8 u |
Cost of 1 necklace = 1 u
Cost of 3 necklaces = 3 u
Cost of 1 ring = 1 u + 41
Cost of 12 rings = 12 x (1 u + 41) = 12 u + 492
Total cost of 3 necklaces and 12 rings
= 3 u + 12 u + 492
= 15 u + 492
15 u + 492 = 1737
15 u = 1737 - 492
15 u = 1245
1 u = 1245 ÷ 15 = 83
Cost of 13 rings = 13(1 u + 41) = 13 u + 533
Cost of 8 necklaces = 8 u
Amount that Jean had at first
= 13 u + 533 + 8 u
= 21 u + 533
= 21 x 83 + 533
= $2276
Answer(s): $2276
