During a sale, 8 necklaces and 3 bracelets cost $2180. If Dana bought 10 necklaces and 6 bracelets, she would have spent all her money. Each necklace cost $146 more than a bracelet. Find the amount that Dana had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
8 |
3 |
10 |
6 |
| Value |
1 u + 146 |
1 u |
1 u + 146 |
1 u |
| Total value |
8 u + 1168 |
3 u |
10 u + 1460 |
6 u |
Cost of 1 bracelet = 1 u
Cost of 3 bracelets = 3 u
Cost of 1 necklace = 1 u + 146
Cost of 8 necklaces = 8 x (1 u + 146) = 8 u + 1168
Total cost of 3 bracelets and 8 necklaces
= 3 u + 8 u + 1168
= 11 u + 1168
11 u + 1168 = 2180
11 u = 2180 - 1168
11 u = 1012
1 u = 1012 ÷ 11 = 92
Cost of 10 necklaces = 10(1 u + 146) = 10 u + 1460
Cost of 6 bracelets = 6 u
Amount that Dana had at first
= 10 u + 1460 + 6 u
= 16 u + 1460
= 16 x 92 + 1460
= $2932
Answer(s): $2932
