During a sale, 7 bracelets and 11 necklaces cost $959. If Jane bought 12 bracelets and 13 necklaces, she would have spent all her money. Each bracelet cost $101 more than a necklace. Find the amount that Jane had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
7 |
11 |
12 |
13 |
| Value |
1 u + 101 |
1 u |
1 u + 101 |
1 u |
| Total value |
7 u + 707 |
11 u |
12 u + 1212 |
13 u |
Cost of 1 necklace = 1 u
Cost of 11 necklaces = 11 u
Cost of 1 bracelet = 1 u + 101
Cost of 7 bracelets = 7 x (1 u + 101) = 7 u + 707
Total cost of 11 necklaces and 7 bracelets
= 11 u + 7 u + 707
= 18 u + 707
18 u + 707 = 959
18 u = 959 - 707
18 u = 252
1 u = 252 ÷ 18 = 14
Cost of 12 bracelets = 12(1 u + 101) = 12 u + 1212
Cost of 13 necklaces = 13 u
Amount that Jane had at first
= 12 u + 1212 + 13 u
= 25 u + 1212
= 25 x 14 + 1212
= $1562
Answer(s): $1562
