During a sale, 3 bracelets and 9 necklaces cost $564. If Winnie bought 15 bracelets and 11 necklaces, she would have spent all her money. Each bracelet cost $112 more than a necklace. Find the amount that Winnie had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
3 |
9 |
15 |
11 |
| Value |
1 u + 112 |
1 u |
1 u + 112 |
1 u |
| Total value |
3 u + 336 |
9 u |
15 u + 1680 |
11 u |
Cost of 1 necklace = 1 u
Cost of 9 necklaces = 9 u
Cost of 1 bracelet = 1 u + 112
Cost of 3 bracelets = 3 x (1 u + 112) = 3 u + 336
Total cost of 9 necklaces and 3 bracelets
= 9 u + 3 u + 336
= 12 u + 336
12 u + 336 = 564
12 u = 564 - 336
12 u = 228
1 u = 228 ÷ 12 = 19
Cost of 15 bracelets = 15(1 u + 112) = 15 u + 1680
Cost of 11 necklaces = 11 u
Amount that Winnie had at first
= 15 u + 1680 + 11 u
= 26 u + 1680
= 26 x 19 + 1680
= $2174
Answer(s): $2174
