[email protected] wrote:A painter wishes to paint a house turquoise. To make the color, he selects an eggshell primer made up of 70% pure-white color, and combines it with a blue base coat in order to create a turquoise color made up of 75% pure-white. How many quarts from the blue base coat should be mixed to make enough turquoise to paint the house?
1.It will take 300 quarts of paint to cover the house.

2.The blue base-coat is made up of 90% pure-white color.

[spoiler]Ans-C
[/spoiler]

We are to answer:

How many quarts from the blue base coat should be mixed to make enough turquoise to paint the house?

We know that the eggshell primer is made up of 70% pure-white color and the blue base coat is combined in order to create a turquoise color made up of 75% pure-white. We further know that these two are the only ingredients for the turquoise.

In order to answer the DS from here, we need to know:

"¢ How many quart of paint is required to paint the house turquoise?

"¢ In what proportion the two ingredients are mixed?

"¢ What is the concentration of pure-white color in the blue base coat?

Over to statements

(1) It will take 300 quarts of paint to cover the house. This is one of our three basic needs, insufficient.

(2) The blue base-coat is made up of 90% pure-white color. This is one of our three basic needs, insufficient.

When taken together, we can first apply the alligation rule in (2) to find the ratio in the quantities in which the two ingredients should be mixed, and next, with the help of (1), solve for the answer.

[spoiler]Hence C[/spoiler]

Let's say W = the # of quarts of eggshell primer and B = # of quarts of blue base. We also know that .7W = the # of quarts of pure-white color in the eggshell primer, and that

.7W + (x% of B) = .75(W+B), where x is the percentage of the blue base that is pure white.

S1 tells us that W + B = 300. This gives us .7W + (x% of B) = .75(300), but we can't solve for B.
S2 tells us that x = 90. This gives us .7W + .9B = .75(W+B), or .05W = .15B, or W = 3B. This helps too, but we still can't solve for B.

S1+S2 tells us that W + B = 300 and that W = 3B. So W = 225, B = 75, and we're set!

[email protected] wrote:A painter wishes to paint a house turquoise. To make the color, he selects an eggshell primer made up of 70% pure-white color, and combines it with a blue base coat in order to create a turquoise color made up of 75% pure-white. How many quarts from the blue base coat should be mixed to make enough turquoise to paint the house?
1.It will take 300 quarts of paint to cover the house.

2.The blue base-coat is made up of 90% pure-white color.

[spoiler]Ans-C
[/spoiler]

alligiation aproach

from 1&2

from 2 70----75---90
5 15
reverse the order
15 5
from here we require 3/4 of egg shell and 1/4 of blue base

for excat ammount of quarte we need total ammount from 1st

3/4*300 of eggshell and 1/4*300 of blue base