During a sale, 9 bracelets and 5 necklaces cost $1353. If Nora bought 11 bracelets and 13 necklaces, she would have spent all her money. Each bracelet cost $43 more than a necklace. Find the amount that Nora had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
9 |
5 |
11 |
13 |
| Value |
1 u + 43 |
1 u |
1 u + 43 |
1 u |
| Total value |
9 u + 387 |
5 u |
11 u + 473 |
13 u |
Cost of 1 necklace = 1 u
Cost of 5 necklaces = 5 u
Cost of 1 bracelet = 1 u + 43
Cost of 9 bracelets = 9 x (1 u + 43) = 9 u + 387
Total cost of 5 necklaces and 9 bracelets
= 5 u + 9 u + 387
= 14 u + 387
14 u + 387 = 1353
14 u = 1353 - 387
14 u = 966
1 u = 966 ÷ 14 = 69
Cost of 11 bracelets = 11(1 u + 43) = 11 u + 473
Cost of 13 necklaces = 13 u
Amount that Nora had at first
= 11 u + 473 + 13 u
= 24 u + 473
= 24 x 69 + 473
= $2129
Answer(s): $2129
