During a sale, 8 necklaces and 12 rings cost $1836. If Penelope bought 6 necklaces and 14 rings, she would have spent all her money. Each necklace cost $37 more than a ring. Find the amount that Penelope had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
8 |
12 |
6 |
14 |
| Value |
1 u + 37 |
1 u |
1 u + 37 |
1 u |
| Total value |
8 u + 296 |
12 u |
6 u + 222 |
14 u |
Cost of 1 ring = 1 u
Cost of 12 rings = 12 u
Cost of 1 necklace = 1 u + 37
Cost of 8 necklaces = 8 x (1 u + 37) = 8 u + 296
Total cost of 12 rings and 8 necklaces
= 12 u + 8 u + 296
= 20 u + 296
20 u + 296 = 1836
20 u = 1836 - 296
20 u = 1540
1 u = 1540 ÷ 20 = 77
Cost of 6 necklaces = 6(1 u + 37) = 6 u + 222
Cost of 14 rings = 14 u
Amount that Penelope had at first
= 6 u + 222 + 14 u
= 20 u + 222
= 20 x 77 + 222
= $1762
Answer(s): $1762
