Question

Tom purchases 4 gallons of paint and three brushes for $95. Stacy bought two gallon of paint and four brushes for $60 what is the cost of each gallon of paint

Answer 1

A gallon of paints costs $20.00

Explanation:

Let g = the cost for a of gallons of pains

Let b = the cost of a brush

4g + 3b = 95

2g + 4b = 60 ⇒ multiply by negative 2 ⇒ -4g - 8b = -120

Add the two bold equations together

4g + 3b = 95

-4g - 8b = -120

-5b = -25 Divide both sides by -5

b = 5

The cost of the brushes is $5.00 each.

Substitutes 5 for b in the first equation and solve for g. You could use either equation

4g + 3b = 95

4g + 3(5) = 98

4g + 15 = 95 Subtract 15 from both sides

4g + 15 - 15 = 95 - 15

4g = 80 Divide both sides by 4

g = 20

A gallon of paints costs $20.00

Check:

4g + 3b = 95

4(20) + 3(5) = 95

80 + 15 = 95

95 = 95 checks

2g + 4b = 60

2(20) + 4(5) = 60

40 + 20 = 60

60 = 60 checks