During a sale, 5 bracelets and 3 necklaces cost $890. If Mary bought 6 bracelets and 14 necklaces, she would have spent all her money. Each bracelet cost $34 more than a necklace. Find the amount that Mary had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
5 |
3 |
6 |
14 |
| Value |
1 u + 34 |
1 u |
1 u + 34 |
1 u |
| Total value |
5 u + 170 |
3 u |
6 u + 204 |
14 u |
Cost of 1 necklace = 1 u
Cost of 3 necklaces = 3 u
Cost of 1 bracelet = 1 u + 34
Cost of 5 bracelets = 5 x (1 u + 34) = 5 u + 170
Total cost of 3 necklaces and 5 bracelets
= 3 u + 5 u + 170
= 8 u + 170
8 u + 170 = 890
8 u = 890 - 170
8 u = 720
1 u = 720 ÷ 8 = 90
Cost of 6 bracelets = 6(1 u + 34) = 6 u + 204
Cost of 14 necklaces = 14 u
Amount that Mary had at first
= 6 u + 204 + 14 u
= 20 u + 204
= 20 x 90 + 204
= $2004
Answer(s): $2004
