During a sale, 6 necklaces and 9 bracelets cost $714. If Barbara bought 10 necklaces and 12 bracelets, she would have spent all her money. Each necklace cost $69 more than a bracelet. Find the amount that Barbara had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
6 |
9 |
10 |
12 |
| Value |
1 u + 69 |
1 u |
1 u + 69 |
1 u |
| Total value |
6 u + 414 |
9 u |
10 u + 690 |
12 u |
Cost of 1 bracelet = 1 u
Cost of 9 bracelets = 9 u
Cost of 1 necklace = 1 u + 69
Cost of 6 necklaces = 6 x (1 u + 69) = 6 u + 414
Total cost of 9 bracelets and 6 necklaces
= 9 u + 6 u + 414
= 15 u + 414
15 u + 414 = 714
15 u = 714 - 414
15 u = 300
1 u = 300 ÷ 15 = 20
Cost of 10 necklaces = 10(1 u + 69) = 10 u + 690
Cost of 12 bracelets = 12 u
Amount that Barbara had at first
= 10 u + 690 + 12 u
= 22 u + 690
= 22 x 20 + 690
= $1130
Answer(s): $1130
