During a sale, 10 necklaces and 11 rings cost $1280. If Linda bought 9 necklaces and 5 rings, she would have spent all her money. Each necklace cost $86 more than a ring. Find the amount that Linda had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Rings |
Necklaces |
Rings |
| Number |
10 |
11 |
9 |
5 |
| Value |
1 u + 86 |
1 u |
1 u + 86 |
1 u |
| Total value |
10 u + 860 |
11 u |
9 u + 774 |
5 u |
Cost of 1 ring = 1 u
Cost of 11 rings = 11 u
Cost of 1 necklace = 1 u + 86
Cost of 10 necklaces = 10 x (1 u + 86) = 10 u + 860
Total cost of 11 rings and 10 necklaces
= 11 u + 10 u + 860
= 21 u + 860
21 u + 860 = 1280
21 u = 1280 - 860
21 u = 420
1 u = 420 ÷ 21 = 20
Cost of 9 necklaces = 9(1 u + 86) = 9 u + 774
Cost of 5 rings = 5 u
Amount that Linda had at first
= 9 u + 774 + 5 u
= 14 u + 774
= 14 x 20 + 774
= $1054
Answer(s): $1054
