During a sale, 8 rings and 7 bracelets cost $2033. If Sarah bought 4 rings and 9 bracelets, she would have spent all her money. Each ring cost $136 more than a bracelet. Find the amount that Sarah had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
8 |
7 |
4 |
9 |
| Value |
1 u + 136 |
1 u |
1 u + 136 |
1 u |
| Total value |
8 u + 1088 |
7 u |
4 u + 544 |
9 u |
Cost of 1 bracelet = 1 u
Cost of 7 bracelets = 7 u
Cost of 1 ring = 1 u + 136
Cost of 8 rings = 8 x (1 u + 136) = 8 u + 1088
Total cost of 7 bracelets and 8 rings
= 7 u + 8 u + 1088
= 15 u + 1088
15 u + 1088 = 2033
15 u = 2033 - 1088
15 u = 945
1 u = 945 ÷ 15 = 63
Cost of 4 rings = 4(1 u + 136) = 4 u + 544
Cost of 9 bracelets = 9 u
Amount that Sarah had at first
= 4 u + 544 + 9 u
= 13 u + 544
= 13 x 63 + 544
= $1363
Answer(s): $1363
