math problems

Question

a contractor pays $30 per gallon for varnish, and $25 per gallon for paint. the contractor recently spent $1075 for paint and varnish, buying ten more gallons of paint and than varnish. how many gallons of each did the contractor buy?

Answer 1

Hi Tom,

 

Let's begin by writing expressions for our two unknowns based upon the information given in the problem:

    x = # of gal. of varnish

    x + 10 = # of gal. of paint

 

Next, let's write an equation to express the total cost of the varnish and paint in terms of the cost per gallon of each and our unknown quantity of each and then solve the equation for our unknown quantities:

    30x + 25(x + 10) = 1075

    30x + 25x + 250 = 1075

             55x + 250 = 1075

                      55x = 1075 - 250

                      55x = 825

                         x = 825/55

                         x = 15 gal. of varnish

                  x + 10 = 15 + 10

                  x + 10 = 25 gal. of paint

 

Finally, we can check our answers by plugging both quantities into our equation and see if the sum of the two purchases equals the cost of the total purchase:

    30x + 25(x + 10) = 1075

    30(15) + 25(25) = 1075

    450 + 625 = 1075

            1075 = 1075 (2 purchases = total purchase)

 

Since the sum of the two purchases equals the cost of the total purchase, we are confident that our answers for the two quantities are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.