Question

A shade of paint is made by evenly mixing m gallons of white paint, costing $12 a gallon, with n gallons of blue paint, costing $30. What is the cost, in dollars per gallon, of the resulting mixture?

Answer 1

The cost of mixture is

`(12m + 30n)/(m+n)\text{ dollars per gallon}`

Explanation:

We are given the following in the question:

Cost of white per gallon = $12 a gallon

Amount of white paint in the mixture = m gallons

Total cost of white paint =

`12* m = 12m\$`

Cost of blue per gallon = $30 a gallon

Amount of blue paint in the mixture = n gallons

Total cost of blue paint =

`30* n = 30n\$`

Total cost of mixture =

Total cost of white paint + Total cost of blue paint

`(12m + 30n)\text{ dollars}`

Total amount of mixture =

Amount of white paint in the mixture + Amount of blue paint in the mixture

`=(m+n)\text{ gallons}`

Cost of mixture per gallon =

`=\frac{\text{Total cost}}{\text{Total amount}}\\\\=(12m + 30n)/(m+n)\text{ dollars per gallon}`

is the required cost of mixture.