During a sale, 11 necklaces and 7 rings cost $1856. If Hazel bought 4 necklaces and 15 rings, she would have spent all her money. Each necklace cost $100 more than a ring. Find the amount that Hazel had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
11 |
7 |
4 |
15 |
| Value |
1 u + 100 |
1 u |
1 u + 100 |
1 u |
| Total value |
11 u + 1100 |
7 u |
4 u + 400 |
15 u |
Cost of 1 ring = 1 u
Cost of 7 rings = 7 u
Cost of 1 necklace = 1 u + 100
Cost of 11 necklaces = 11 x (1 u + 100) = 11 u + 1100
Total cost of 7 rings and 11 necklaces
= 7 u + 11 u + 1100
= 18 u + 1100
18 u + 1100 = 1856
18 u = 1856 - 1100
18 u = 756
1 u = 756 ÷ 18 = 42
Cost of 4 necklaces = 4(1 u + 100) = 4 u + 400
Cost of 15 rings = 15 u
Amount that Hazel had at first
= 4 u + 400 + 15 u
= 19 u + 400
= 19 x 42 + 400
= $1198
Answer(s): $1198
