Paint costs $21 per gallon is to be mixed with 6 gallons of paint thinner costing $5 per gallon to make a paint that can be $15 per gallon. Compute how much paint mixture will be produced.
Let the quantity of paint be x gallons, then
cost of paint = $21x
cost of thinner = 6*$5
cost of mixture = $15*(x+6)
therefore
21x+6*5 = 15(x+6)
Solve for x.
10
To find out how much paint mixture will be produced, we need to determine the ratio of paint to paint thinner in the final mixture.
Let's assume that 'x' gallons of paint will be mixed with the 6 gallons of paint thinner.
The cost of the paint before mixing will be the cost of the paint after mixing, since the final mixture is priced at $15 per gallon. Therefore, we can equate the costs:
Cost of paint = Cost of final mixture
$21x + $5(6) = $15(x + 6)
Next, we can solve this equation to find the value of 'x':
$21x + $30 = $15x + $90
Subtract $15x from both sides:
$6x + $30 = $90
Subtract $30 from both sides:
$6x = $60
Divide both sides by $6:
x = $10
Hence, 'x' represents the number of gallons of paint needed to be mixed with the 6 gallons of paint thinner.
To determine the total amount of mixture produced, we add the amount of paint to the amount of paint thinner:
Total mixture = x (paint) + 6 (paint thinner)
Total mixture = 10 gallons + 6 gallons
Total mixture = 16 gallons
Therefore, 16 gallons of paint mixture will be produced.