/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 259 In the following exercises, tran... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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

01

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.

02

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 is65脳0.15=9.75

And the total amount of solution can be expressed as0.25x+0.12y=9.75--(2)

03

Step 3. Calculation   

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

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

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

0.25x+0.25y-0.25x-0.12y=16.25-9.750.13y=6.5y=50

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

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following exercises, translate to a system of equations and solve.

Sarah left Minneapolis heading east on the interstate at a speed of 60 mph. Her sister followed her on the same route, leaving two hours later and driving at a rate of 70 mph. How long will it take for Sarah鈥檚 sister to catch up to Sarah.

In the following exercises, solve the following systems of equations by graphing.

x+y=6x-y=-8

In the following exercises, solve the systems of equations by substitution.

2x-15y=712x+2y=-4

In the following exercises, translate to a system of equations and solve.

The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles.

In the following exercises, translate to a system of equations and solve.

The sum of two numbers is -26. One number is 12 less than the other. Find the numbers.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.