A shade of paint is made by evenly mixing m gallons of white paint, co

Question

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

A.  12m +30n

B.  42(12m +30n)

C.  \frac{(12m +30n)}{42}

D.  \frac{(12m +30n)}{(m+ n)}

E.  \frac{42(m + n)}{(12m +30n)}

TestPrepUnlimited · Answer

We need to know two things: Total cost, and the total amount of paint in gallons. With these, we can calculate the average cost.

The white paint costs 12 * m in total, all the blue paint costs 30 * n in total. So total cost = 12 * m + 30 * n.
Total amount of paint in gallons = m + n.

Therefore the average cost is (12m + 30n) / (m + n).

Ans: D

harshbirsingh · Answer

The question is basically asking us to calculate the weighted average cost of the mixture.

Weighted average cost = total cost / total weight.

Total cost = (m*12 + n*30)

Total weight = m+n

As such, weight average cost = (m*12+n*30)/(m+n)

Option D

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dave13 · Answer

) TestPrepUnlimited wait a second, if you buy 2 litres of white and 2 litres of blue paint. So (12 *2) +(30*2) = 84 so the cost is 84 EUR for mixture. If someone asked you what is the cost you payed for it ? wouldnt you answer 84 EUR ?

The question doesnt ask about average cost , it just askes the about the cost. If my reasoning is not correct then in what case would Option A be correct ?

TestPrepUnlimited · Answer

The question asks for the cost in dollars per gallon. Answer A is the total cost of the m+n gallon mixture.

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dave13 · Answer

thank you for quick and clear response

Paras96 · Answer

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

Total cost of mixture = m+n
Total cost of mixture = 12m+30n

Cost/gallon = Total cost of mixture/Total cost of mixture =  /

Hence D

A shade of paint is made by evenly mixing m gallons of white paint, co

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A shade of paint is made by evenly mixing m gallons of white paint, co

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