During a sale, 3 necklaces and 10 bracelets cost $297. If Joelle bought 15 necklaces and 9 bracelets, she would have spent all her money. Each necklace cost $34 more than a bracelet. Find the amount that Joelle had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
3 |
10 |
15 |
9 |
| Value |
1 u + 34 |
1 u |
1 u + 34 |
1 u |
| Total value |
3 u + 102 |
10 u |
15 u + 510 |
9 u |
Cost of 1 bracelet = 1 u
Cost of 10 bracelets = 10 u
Cost of 1 necklace = 1 u + 34
Cost of 3 necklaces = 3 x (1 u + 34) = 3 u + 102
Total cost of 10 bracelets and 3 necklaces
= 10 u + 3 u + 102
= 13 u + 102
13 u + 102 = 297
13 u = 297 - 102
13 u = 195
1 u = 195 ÷ 13 = 15
Cost of 15 necklaces = 15(1 u + 34) = 15 u + 510
Cost of 9 bracelets = 9 u
Amount that Joelle had at first
= 15 u + 510 + 9 u
= 24 u + 510
= 24 x 15 + 510
= $870
Answer(s): $870
