During a sale, 10 necklaces and 6 rings cost $1872. If Cindy bought 11 necklaces and 4 rings, she would have spent all her money. Each necklace cost $144 more than a ring. Find the amount that Cindy had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
10 |
6 |
11 |
4 |
| Value |
1 u + 144 |
1 u |
1 u + 144 |
1 u |
| Total value |
10 u + 1440 |
6 u |
11 u + 1584 |
4 u |
Cost of 1 ring = 1 u
Cost of 6 rings = 6 u
Cost of 1 necklace = 1 u + 144
Cost of 10 necklaces = 10 x (1 u + 144) = 10 u + 1440
Total cost of 6 rings and 10 necklaces
= 6 u + 10 u + 1440
= 16 u + 1440
16 u + 1440 = 1872
16 u = 1872 - 1440
16 u = 432
1 u = 432 ÷ 16 = 27
Cost of 11 necklaces = 11(1 u + 144) = 11 u + 1584
Cost of 4 rings = 4 u
Amount that Cindy had at first
= 11 u + 1584 + 4 u
= 15 u + 1584
= 15 x 27 + 1584
= $1989
Answer(s): $1989
