During a sale, 6 necklaces and 10 bracelets cost $1364. If Tiffany bought 13 necklaces and 14 bracelets, she would have spent all her money. Each necklace cost $46 more than a bracelet. Find the amount that Tiffany had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
6 |
10 |
13 |
14 |
| Value |
1 u + 46 |
1 u |
1 u + 46 |
1 u |
| Total value |
6 u + 276 |
10 u |
13 u + 598 |
14 u |
Cost of 1 bracelet = 1 u
Cost of 10 bracelets = 10 u
Cost of 1 necklace = 1 u + 46
Cost of 6 necklaces = 6 x (1 u + 46) = 6 u + 276
Total cost of 10 bracelets and 6 necklaces
= 10 u + 6 u + 276
= 16 u + 276
16 u + 276 = 1364
16 u = 1364 - 276
16 u = 1088
1 u = 1088 ÷ 16 = 68
Cost of 13 necklaces = 13(1 u + 46) = 13 u + 598
Cost of 14 bracelets = 14 u
Amount that Tiffany had at first
= 13 u + 598 + 14 u
= 27 u + 598
= 27 x 68 + 598
= $2434
Answer(s): $2434
