During a sale, 6 rings and 4 necklaces cost $428. If Xandra bought 11 rings and 4 necklaces, she would have spent all her money. Each ring cost $38 more than a necklace. Find the amount that Xandra had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
6 |
4 |
11 |
4 |
| Value |
1 u + 38 |
1 u |
1 u + 38 |
1 u |
| Total value |
6 u + 228 |
4 u |
11 u + 418 |
4 u |
Cost of 1 necklace = 1 u
Cost of 4 necklaces = 4 u
Cost of 1 ring = 1 u + 38
Cost of 6 rings = 6 x (1 u + 38) = 6 u + 228
Total cost of 4 necklaces and 6 rings
= 4 u + 6 u + 228
= 10 u + 228
10 u + 228 = 428
10 u = 428 - 228
10 u = 200
1 u = 200 ÷ 10 = 20
Cost of 11 rings = 11(1 u + 38) = 11 u + 418
Cost of 4 necklaces = 4 u
Amount that Xandra had at first
= 11 u + 418 + 4 u
= 15 u + 418
= 15 x 20 + 418
= $718
Answer(s): $718
