how do I set up this word problem to solve

Question

Paint costing $19 per gallon is to be mixed with thinner costing $3 per gallon. How much of each should be added to make 16 gallons of a mix that costs $14 per gallon?

Answer 1

Hi Barbara

 

Let's define some variables

 

P = gallons of paint

T = gallons of thinner

 

P + T = 16                We will have a mixture of a total of 16 gallons

19P + 3T = 14(16)    The cost of paint if $19/gal and the cost of the thinner is $3/gal.  Together we have a mixture of 16 gallons at $14/gallon

 

We have a systems of equations, which you can solve

    P +   T = 16
19P + 3T = 14(16)