During a sale, 8 necklaces and 4 bracelets cost $1384. If Eva bought 10 necklaces and 11 bracelets, she would have spent all her money. Each necklace cost $86 more than a bracelet. Find the amount that Eva had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
8 |
4 |
10 |
11 |
| Value |
1 u + 86 |
1 u |
1 u + 86 |
1 u |
| Total value |
8 u + 688 |
4 u |
10 u + 860 |
11 u |
Cost of 1 bracelet = 1 u
Cost of 4 bracelets = 4 u
Cost of 1 necklace = 1 u + 86
Cost of 8 necklaces = 8 x (1 u + 86) = 8 u + 688
Total cost of 4 bracelets and 8 necklaces
= 4 u + 8 u + 688
= 12 u + 688
12 u + 688 = 1384
12 u = 1384 - 688
12 u = 696
1 u = 696 ÷ 12 = 58
Cost of 10 necklaces = 10(1 u + 86) = 10 u + 860
Cost of 11 bracelets = 11 u
Amount that Eva had at first
= 10 u + 860 + 11 u
= 21 u + 860
= 21 x 58 + 860
= $2078
Answer(s): $2078
