During a sale, 5 bracelets and 9 rings cost $1001. If Diana bought 12 bracelets and 5 rings, she would have spent all her money. Each bracelet cost $21 more than a ring. Find the amount that Diana had at first.
|
Case 1 |
Case 2 |
|
Bracelets |
Rings |
Bracelets |
Rings |
Number |
5 |
9 |
12 |
5 |
Value |
1 u + 21 |
1 u |
1 u + 21 |
1 u |
Total value |
5 u + 105 |
9 u |
12 u + 252 |
5 u |
Cost of 1 ring = 1 u
Cost of 9 rings = 9 u
Cost of 1 bracelet = 1 u + 21
Cost of 5 bracelets = 5 x (1 u + 21) = 5 u + 105
Total cost of 9 rings and 5 bracelets
= 9 u + 5 u + 105
= 14 u + 105
14 u + 105 = 1001
14 u = 1001 - 105
14 u = 896
1 u = 896 ÷ 14 = 64
Cost of 12 bracelets = 12(1 u + 21) = 12 u + 252
Cost of 5 rings = 5 u
Amount that Diana had at first
= 12 u + 252 + 5 u
= 17 u + 252
= 17 x 64 + 252
= $1340
Answer(s): $1340