During a sale, 11 necklaces and 12 bracelets cost $1654. If Anna bought 11 necklaces and 9 bracelets, she would have spent all her money. Each necklace cost $27 more than a bracelet. Find the amount that Anna had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
11 |
12 |
11 |
9 |
| Value |
1 u + 27 |
1 u |
1 u + 27 |
1 u |
| Total value |
11 u + 297 |
12 u |
11 u + 297 |
9 u |
Cost of 1 bracelet = 1 u
Cost of 12 bracelets = 12 u
Cost of 1 necklace = 1 u + 27
Cost of 11 necklaces = 11 x (1 u + 27) = 11 u + 297
Total cost of 12 bracelets and 11 necklaces
= 12 u + 11 u + 297
= 23 u + 297
23 u + 297 = 1654
23 u = 1654 - 297
23 u = 1357
1 u = 1357 ÷ 23 = 59
Cost of 11 necklaces = 11(1 u + 27) = 11 u + 297
Cost of 9 bracelets = 9 u
Amount that Anna had at first
= 11 u + 297 + 9 u
= 20 u + 297
= 20 x 59 + 297
= $1477
Answer(s): $1477
