During a sale, 6 bracelets and 7 necklaces cost $1364. If Irene bought 7 bracelets and 6 necklaces, she would have spent all her money. Each bracelet cost $93 more than a necklace. Find the amount that Irene had at first.
| |
Case 1 |
Case 2 |
| |
Bracelets |
Necklaces |
Bracelets |
Necklaces |
| Number |
6 |
7 |
7 |
6 |
| Value |
1 u + 93 |
1 u |
1 u + 93 |
1 u |
| Total value |
6 u + 558 |
7 u |
7 u + 651 |
6 u |
Cost of 1 necklace = 1 u
Cost of 7 necklaces = 7 u
Cost of 1 bracelet = 1 u + 93
Cost of 6 bracelets = 6 x (1 u + 93) = 6 u + 558
Total cost of 7 necklaces and 6 bracelets
= 7 u + 6 u + 558
= 13 u + 558
13 u + 558 = 1364
13 u = 1364 - 558
13 u = 806
1 u = 806 ÷ 13 = 62
Cost of 7 bracelets = 7(1 u + 93) = 7 u + 651
Cost of 6 necklaces = 6 u
Amount that Irene had at first
= 7 u + 651 + 6 u
= 13 u + 651
= 13 x 62 + 651
= $1457
Answer(s): $1457
