During a sale, 6 bracelets and 12 necklaces cost $894. If Yoko bought 4 bracelets and 15 necklaces, she would have spent all her money. Each bracelet cost $107 more than a necklace. Find the amount that Yoko had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
6 |
12 |
4 |
15 |
| Value |
1 u + 107 |
1 u |
1 u + 107 |
1 u |
| Total value |
6 u + 642 |
12 u |
4 u + 428 |
15 u |
Cost of 1 necklace = 1 u
Cost of 12 necklaces = 12 u
Cost of 1 bracelet = 1 u + 107
Cost of 6 bracelets = 6 x (1 u + 107) = 6 u + 642
Total cost of 12 necklaces and 6 bracelets
= 12 u + 6 u + 642
= 18 u + 642
18 u + 642 = 894
18 u = 894 - 642
18 u = 252
1 u = 252 ÷ 18 = 14
Cost of 4 bracelets = 4(1 u + 107) = 4 u + 428
Cost of 15 necklaces = 15 u
Amount that Yoko had at first
= 4 u + 428 + 15 u
= 19 u + 428
= 19 x 14 + 428
= $694
Answer(s): $694
