How many of each type did she buy?

Question

mrs. greene brought new hardware for her kitchen cabinets. She brought half as many door handles as hinges and 5 fewer drawer knobs than door handles. handles cost $2.50 each, hinges cost $1.35 each, and drawer knobs cost $1.10 each. She spent a total of $51.20. How many of each type of hardware did she buy?

Answer 1

Let's start with door handles being X.  We know we have half as many door handles as we have hinges, ie twice as many hinges, so hinges are 2X.  There are 5 few drawer knobs than door handles so that is X - 5.  Let's map that out:

 

X = door handles

 

2X = hinges

 

X - 5 = drawer knobs

 

multiplying the amounts times the cost and summing them all up will give us the total spent:

 

2.5*X + 1.35 * 2X + 1.10 * (X-5) = 51.20

 

now solve for X

 

2.5X + 2.7X + 1.10X - 5.5 = 51.20

6.3X - 5.5 = 51.20

6.3X = 56.70

X = 9 - number of door handles

2X = 18 - number of hinges

X-5 = 4 - drawer knob

 

You should still go back and check all the math and calculations and see if it adds up to the right total sums

 

All the best 

 

Lori