During a sale, 6 rings and 7 bracelets cost $1378. If Penelope bought 14 rings and 10 bracelets, she would have spent all her money. Each ring cost $65 more than a bracelet. Find the amount that Penelope had at first.
| |
Case 1 |
Case 2 |
| |
Rings |
Bracelets |
Rings |
Bracelets |
| Number |
6 |
7 |
14 |
10 |
| Value |
1 u + 65 |
1 u |
1 u + 65 |
1 u |
| Total value |
6 u + 390 |
7 u |
14 u + 910 |
10 u |
Cost of 1 bracelet = 1 u
Cost of 7 bracelets = 7 u
Cost of 1 ring = 1 u + 65
Cost of 6 rings = 6 x (1 u + 65) = 6 u + 390
Total cost of 7 bracelets and 6 rings
= 7 u + 6 u + 390
= 13 u + 390
13 u + 390 = 1378
13 u = 1378 - 390
13 u = 988
1 u = 988 ÷ 13 = 76
Cost of 14 rings = 14(1 u + 65) = 14 u + 910
Cost of 10 bracelets = 10 u
Amount that Penelope had at first
= 14 u + 910 + 10 u
= 24 u + 910
= 24 x 76 + 910
= $2734
Answer(s): $2734
