During a sale, 10 bracelets and 11 necklaces cost $1453. If Jen bought 6 bracelets and 7 necklaces, she would have spent all her money. Each bracelet cost $13 more than a necklace. Find the amount that Jen had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
10 |
11 |
6 |
7 |
| Value |
1 u + 13 |
1 u |
1 u + 13 |
1 u |
| Total value |
10 u + 130 |
11 u |
6 u + 78 |
7 u |
Cost of 1 necklace = 1 u
Cost of 11 necklaces = 11 u
Cost of 1 bracelet = 1 u + 13
Cost of 10 bracelets = 10 x (1 u + 13) = 10 u + 130
Total cost of 11 necklaces and 10 bracelets
= 11 u + 10 u + 130
= 21 u + 130
21 u + 130 = 1453
21 u = 1453 - 130
21 u = 1323
1 u = 1323 ÷ 21 = 63
Cost of 6 bracelets = 6(1 u + 13) = 6 u + 78
Cost of 7 necklaces = 7 u
Amount that Jen had at first
= 6 u + 78 + 7 u
= 13 u + 78
= 13 x 63 + 78
= $897
Answer(s): $897
