Question

A scientist needs 10 L of a solution that is 60% acid. She has a 50% acid solution and a 90% acid solution she can mix together to make the 60% solution. Let x represent the number of liters of the 50% solution. Let y represent the number of liters of the 90% solution. Which equation represents the total liters of acid that are needed? Question 3 options: x y = 6 x y = 10 0. 5x 0. 9y = 6 0. 5x 0. 9y = 10.

Answer 1

Allegation is a method to find the ratio in which two or more indignant are mixed to produce a mixture or solution.

The equation represents the total liters of acid that are needed is,

$0.5x+0.9y=6$

Thus the option 3 is the correct option.

What is allegation?

Allegation is a method to find the ratio in which two or more indignant are mixed to produce a mixture or solution.

Given information-

A scientist needs 10 L of a solution that is 60% acid.

The percentage of two acid solution are 50% and 90%.

Variable x represent the number of liters of the 50% solution.

Variable y represent the number of liters of the 90% solution.

Quantity of acid from 50% solution is $0.5x$ liters, and quantity of acid from 90% solution is $0.9x$ liters.

As the scientist needs 10 L of a solution that is 60% acid. Therefore the quantity of acid in 60 percent acid solution is,

$a=10\times\dfrac{60}{100} \\a=6$

Thus 6 liters of acid required by the scientist. As to get the 6 liters of acid from 50% and 90 percent solution, we need to add the amount of acid in these solutions.Thus,

$0.5x+0.9y=6$

This is the required equation.

Hence the equation represents the total liters of acid that are needed is,

$0.5x+0.9y=6$

Thus the option 3 is the correct option.

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