During a sale, 6 rings and 4 bracelets cost $1574. If Cathy bought 10 rings and 15 bracelets, she would have spent all her money. Each ring cost $129 more than a bracelet. Find the amount that Cathy had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
6 |
4 |
10 |
15 |
| Value |
1 u + 129 |
1 u |
1 u + 129 |
1 u |
| Total value |
6 u + 774 |
4 u |
10 u + 1290 |
15 u |
Cost of 1 bracelet = 1 u
Cost of 4 bracelets = 4 u
Cost of 1 ring = 1 u + 129
Cost of 6 rings = 6 x (1 u + 129) = 6 u + 774
Total cost of 4 bracelets and 6 rings
= 4 u + 6 u + 774
= 10 u + 774
10 u + 774 = 1574
10 u = 1574 - 774
10 u = 800
1 u = 800 ÷ 10 = 80
Cost of 10 rings = 10(1 u + 129) = 10 u + 1290
Cost of 15 bracelets = 15 u
Amount that Cathy had at first
= 10 u + 1290 + 15 u
= 25 u + 1290
= 25 x 80 + 1290
= $3290
Answer(s): $3290
