How much does each gallon of paint and each brush cost?

Question

You purchase 8 gallons if paint and 3 brushes for $152.50. The next day, you purchase 6 gallons of paint and 3 brushes for $113.00. How much does each gallon of paint and each brush cost?

Answer 1

The information provided in this problem can be used to develop two equations with two unknowns:

Let P be the price of a gallon of paint and B be the price of a brush.

We have:

1) 8P + 3B = 152.50

2) 6P + 3B = 113.00

 

we can subtract equation 2 from 1 to remove the paint brushes as a factor yielding

2P = 152.5 - 113 = 39.5

or P = 19.75

 

then we can replace P for 19.75 in equation 2:

6(19.75) + 3B = 113.00

118.5 + 3B = 113

 

We now see either the information given is incorect at the outset or the price of a paint brush is negative- one receives value on removing paint brushes from the store inventory over and above the use of the paint brush.

 

Here 3B = 113 - 118.5 = minus 5.5 or B = minus 11/6

 

one can test the particular solution to this system of equations as:

 

8(19.75) +3(-11/6) = 158 - 5.5 = 152.5 as given in equation 1 which matches the data given.

 

one can add subtract multipy and divide equations just like numbers to remove factors, in this case the contribution to the total shopping spree due to the purchase of the brushes.