During a sale, 6 necklaces and 11 bracelets cost $1777. If Roshel bought 8 necklaces and 7 bracelets, she would have spent all her money. Each necklace cost $112 more than a bracelet. Find the amount that Roshel had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
6 |
11 |
8 |
7 |
| Value |
1 u + 112 |
1 u |
1 u + 112 |
1 u |
| Total value |
6 u + 672 |
11 u |
8 u + 896 |
7 u |
Cost of 1 bracelet = 1 u
Cost of 11 bracelets = 11 u
Cost of 1 necklace = 1 u + 112
Cost of 6 necklaces = 6 x (1 u + 112) = 6 u + 672
Total cost of 11 bracelets and 6 necklaces
= 11 u + 6 u + 672
= 17 u + 672
17 u + 672 = 1777
17 u = 1777 - 672
17 u = 1105
1 u = 1105 ÷ 17 = 65
Cost of 8 necklaces = 8(1 u + 112) = 8 u + 896
Cost of 7 bracelets = 7 u
Amount that Roshel had at first
= 8 u + 896 + 7 u
= 15 u + 896
= 15 x 65 + 896
= $1871
Answer(s): $1871
