Chapter 5: Q. 259 (page 659)

In the following exercises, translate to a system of equations and solve.
A scientist needs 65 liters of a 15% alcohol solution. She has available a 25% and a 12% solution. How many liters of the 25% and how many liters of the 12% solutions should she mix to make the 15% solution?

Short Answer

Expert verified

The number of 25% solution is 15 litres and number of 12% solution is 50 litres.

Step by step solution

Step 1. Given Information

The given data is that scientist needs 65 liters of a 15% alcohol solution. She has available a 25% and a 12% solution.

Step 2. Explanation

Let number of units of 25% solution be x and number of units of 12% solution be y.

The number of units of 15% solution is 65 liters.

Thus, the total units of solution can be expressed as $x + y = 65 - - (1)$

The amount of 15% solution is $65 \times 0.15 = 9.75$

And the total amount of solution can be expressed as $0.25 x + 0.12 y = 9.75 - - (2)$

Step 3. Calculation

Multiply equation (1) with number $0.25$ and write the revised equation.

$0.25 (x + y) = 0.25 (65) 0.25 x + 0.25 y = 16.25 - - (3)$

Solve the equation (3) and (2) by subtracting equation (2) from equation (3).

$0.25 x + 0.25 y - 0.25 x - 0.12 y = 16.25 - 9.75 0.13 y = 6.5 y = 50$

Substitute the value of y in equation (1) to find the value of x.

$x + y = 65 x = 65 - 50 x = 15$

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In the following exercises, translate to a system of equations and solve.
A scientist needs 65 liters of a 15% alcohol solution. She has available a 25% and a 12% solution. How many liters of the 25% and how many liters of the 12% solutions should she mix to make the 15% solution?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation

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In the following exercises, translate to a system of equations and solve. A scientist needs 65 liters of a 15% alcohol solution. She has available a 25% and a 12% solution. How many liters of the 25% and how many liters of the 12% solutions should she mix to make the 15% solution?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, translate to a system of equations and solve.
A scientist needs 65 liters of a 15% alcohol solution. She has available a 25% and a 12% solution. How many liters of the 25% and how many liters of the 12% solutions should she mix to make the 15% solution?