During a sale, 7 rings and 12 bracelets cost $2827. If Xandra bought 3 rings and 6 bracelets, she would have spent all her money. Each ring cost $146 more than a bracelet. Find the amount that Xandra had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
7 |
12 |
3 |
6 |
| Value |
1 u + 146 |
1 u |
1 u + 146 |
1 u |
| Total value |
7 u + 1022 |
12 u |
3 u + 438 |
6 u |
Cost of 1 bracelet = 1 u
Cost of 12 bracelets = 12 u
Cost of 1 ring = 1 u + 146
Cost of 7 rings = 7 x (1 u + 146) = 7 u + 1022
Total cost of 12 bracelets and 7 rings
= 12 u + 7 u + 1022
= 19 u + 1022
19 u + 1022 = 2827
19 u = 2827 - 1022
19 u = 1805
1 u = 1805 ÷ 19 = 95
Cost of 3 rings = 3(1 u + 146) = 3 u + 438
Cost of 6 bracelets = 6 u
Amount that Xandra had at first
= 3 u + 438 + 6 u
= 9 u + 438
= 9 x 95 + 438
= $1293
Answer(s): $1293
