During a sale, 7 bracelets and 12 necklaces cost $2478. If Kathy bought 12 bracelets and 11 necklaces, she would have spent all her money. Each bracelet cost $145 more than a necklace. Find the amount that Kathy had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
7 |
12 |
12 |
11 |
| Value |
1 u + 145 |
1 u |
1 u + 145 |
1 u |
| Total value |
7 u + 1015 |
12 u |
12 u + 1740 |
11 u |
Cost of 1 necklace = 1 u
Cost of 12 necklaces = 12 u
Cost of 1 bracelet = 1 u + 145
Cost of 7 bracelets = 7 x (1 u + 145) = 7 u + 1015
Total cost of 12 necklaces and 7 bracelets
= 12 u + 7 u + 1015
= 19 u + 1015
19 u + 1015 = 2478
19 u = 2478 - 1015
19 u = 1463
1 u = 1463 ÷ 19 = 77
Cost of 12 bracelets = 12(1 u + 145) = 12 u + 1740
Cost of 11 necklaces = 11 u
Amount that Kathy had at first
= 12 u + 1740 + 11 u
= 23 u + 1740
= 23 x 77 + 1740
= $3511
Answer(s): $3511
