During a sale, 3 rings and 10 necklaces cost $1345. If Shannon bought 11 rings and 3 necklaces, she would have spent all her money. Each ring cost $41 more than a necklace. Find the amount that Shannon had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Necklaces |
Rings |
Necklaces |
| Number |
3 |
10 |
11 |
3 |
| Value |
1 u + 41 |
1 u |
1 u + 41 |
1 u |
| Total value |
3 u + 123 |
10 u |
11 u + 451 |
3 u |
Cost of 1 necklace = 1 u
Cost of 10 necklaces = 10 u
Cost of 1 ring = 1 u + 41
Cost of 3 rings = 3 x (1 u + 41) = 3 u + 123
Total cost of 10 necklaces and 3 rings
= 10 u + 3 u + 123
= 13 u + 123
13 u + 123 = 1345
13 u = 1345 - 123
13 u = 1222
1 u = 1222 ÷ 13 = 94
Cost of 11 rings = 11(1 u + 41) = 11 u + 451
Cost of 3 necklaces = 3 u
Amount that Shannon had at first
= 11 u + 451 + 3 u
= 14 u + 451
= 14 x 94 + 451
= $1767
Answer(s): $1767
