During a sale, 11 necklaces and 9 bracelets cost $801. If Tina bought 5 necklaces and 3 bracelets, she would have spent all her money. Each necklace cost $51 more than a bracelet. Find the amount that Tina had at first.
| |
Case 1 |
Case 2 |
| |
Necklaces |
Bracelets |
Necklaces |
Bracelets |
| Number |
11 |
9 |
5 |
3 |
| Value |
1 u + 51 |
1 u |
1 u + 51 |
1 u |
| Total value |
11 u + 561 |
9 u |
5 u + 255 |
3 u |
Cost of 1 bracelet = 1 u
Cost of 9 bracelets = 9 u
Cost of 1 necklace = 1 u + 51
Cost of 11 necklaces = 11 x (1 u + 51) = 11 u + 561
Total cost of 9 bracelets and 11 necklaces
= 9 u + 11 u + 561
= 20 u + 561
20 u + 561 = 801
20 u = 801 - 561
20 u = 240
1 u = 240 ÷ 20 = 12
Cost of 5 necklaces = 5(1 u + 51) = 5 u + 255
Cost of 3 bracelets = 3 u
Amount that Tina had at first
= 5 u + 255 + 3 u
= 8 u + 255
= 8 x 12 + 255
= $351
Answer(s): $351
