At a hardware store, 5 gallons of paint and 5 paintbrushes cost $120, while 2 gallons of paint and 6 paintbrushes cost $64. Find the cost of 1 paintbrush.

Question

Please help.

Answer 1

System of simultaneous equations.

Let p = gallons of paint

Let b = brushes

 

5p + 5b = 120   {equation 1}

2p + 6b = 64     {equation 2}

 

Using elimination we can solve for one

variable, then use that to solve for the other.

 

Multiply equation 1 by 2

Multiply equation 2 by -5

Add equations to eliminate variable p

 

10p + 10b = 240    2(equation1)

-10p - 30b = -320    -5(equation 2)

------------------------

        -20b = -80

         b = 4

 

paintbrushes cost $4

Replace b with 4 in one of the original

equations and solve for p

 

2p + 6b = 64

2p + 6(4) = 64

2p + 24 = 64

2p = 40

p = 20

 

A gallon of paint costs $20

Paintbrushes cost $4

Answer 2

System of equations
Elimination method

g= cost of gallons of paint
b= cost of paint brushes

5g+5b=120
2g+6b=64

2(5g+5b=120)
5(2g+6b=64)

10g+10b=240
10g+30b=320

subtract to eliminate

-20b=-80
b=4