SOLUTION: A painter needs a custom color for a large mural he is painting. To make the custom painting he must add four units of blue and 3 units of magenta to each quart of paint. The paint

Question 1172284: A painter needs a custom color for a large mural he is painting. To make the custom painting he must add four units of blue and 3 units of magenta to each quart of paint. The painter knows that a gallon of paint will cover 350 sq ft. He also knows that 4 quarts equals 1 gallon. How many units of magenta will he need for the mural which is 1200 square feet. Round your answer
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
one gallon of paint will cover 350 square feet.
the mural is 1200 square feet.
1200 / 350 = 3.428571429 gallons of paint.
round that up to the nearest gallon and he needs 4 gallons of paint.
round that up to the nearest quart and he needs 3.5 gallons of paint.
to make the custom painting, he must add 4 units of blue and 3 units of magenta for each quart of paint.

the answer to this depends on whether he wants to round this to the nearest quart or to the nearest gallon.
there would arguments for each case.
with the gallon, he has enough left over to patch up spots if there's a problem and he also doesn't have to take the paint out of the gallon container and place it into quart containers before mixing.
with the quart, that's the minimum number of paint that he will need to use that is practical to divide from the gallon container.

if you round to the nearest gallon, 4 gallons is equal to 16 quarts.
4 * 16 of blue and 3 * 16 of magenta means he will need a total of 64 units of blue and 48 units of magenta.

if you round to the nearest quart, 3.5 gallons is equal to 14 quarts.
4 * 14 of blue and 3 * 14 of magenta means he will need a total of 56 units of blue and 42 units of magenta.

since you're only asked for the number of units of magenta, then you answer will be either 48 or 42 units of magenta, depending on what unit he wants to round to, i.e. gallons or quarts.

now, he could buy the paint in quarts if quarts are available, but the price of 4 quarts is usually more than the price of a gallon.

if he had the option, he could buy 3 gallons and 2 quarts, assuming the quarts are available.

the problem here is that you are not told the options he has available, nor the price of each option, so you are left in the dark as to what he would want to do.

i'm probably reading too much into the problem.
without knowing any better, i would go with rounding to the nearest quart.

1200 square feet / 350 = 3.428571429 gallons * 4 quarts to a gallon = 13.71428571 quarts which you would round up to the nearest quart to get 14 quarts.

that's the minimum he will need without taking into account the cost of a quart versus the cost of a gallon.

with that in mind, go for 56 units of blue and 42 units of magenta as the minimum he would need.

Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.

The ratio of the areas is 1200/350 = 24/7. So, the ratio of the paint volumes is 24/7, too. The number of units of magenta is 3 per each quart, or 3*4 = 12 units per gallon. Hence, the number of units of magenta is 24/7 times 12, or = = 41 for the mural of 1200 sq ft. Round it as you want.

Solved.

That's all.

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