how to solve

Question

Brian McDevitt, REAL suspect in the robbery of the ISG Museum, went on an odd shopping spree the day before the heist.  He bought a black jacket, a policeman-style cap, and rubber gloves.  He also had a copy made of a key.  The total he spent came to $100.  The interesting clothing purchase was $99 MORE than the cost of the key.  How much did it cost to copy the key?

Answer 1

Let C = cost of clothing

Let K = cost of key

 

Clothing was $99 more than key  ==>  C = K + 99

 

Total spent came to $100  ==>  C + K = 100

 

Substitute the value for C from the 1st equation in to the 2nd equation and solve  

 

(K + 99) + K = 100

2K = 1

K = 1/2 = $0.50

 

The cost to copy the key was $0.50 = 50 cents 

 

To check, note that the clothing cost $99.50 so the total was $100