/*! 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} Problem 62 Write an original word problem t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 62

Write an original word problem that can be solved using a linear equation. Then solve the problem.

Short Answer

Expert verified
A linear equation representing the given situation is \(y= p*x - \frac{50}{3}*x\). By substituting p=80, y=1000 into the equation, it is found that approximately 13 pairs of shoes can be bought with 1000 dollars after discounts.

Step by step solution

01

Formulate Word Problem

The first part of the exercise is to formulate a word problem that can be solved using a linear equation. Consider a situation at a clothing store where for every 3 pairs of shoes purchased, 50 dollars are deducted from the total amount. If x represents the number of pairs of shoes and y the total price after the discount, then y equals the price of one pair of shoes times x(amount of shoes bought) minus 50 dollars for every 3 pairs bought.
02

Create Linear Equation

Next, formulate the system of linear equations based on the situation in the problem. If the price of a pair of shoes is assumed to be p, then the total price after discount, y, can be determined by the following linear equation: \(y = p*x - \frac{50}{3}*x\)
03

Solve the Equation

Now suppose the price of a pair of shoes is 80 dollars and the goal is to find how many pairs of shoes can be bought for 1000 dollars. Substitute p=80, y=1000 in the equation to find x: \(1000 = 80*x - \frac{50}{3}*x\). Solving this equation for x, we find that approximately 13.7 pairs of shoes can be bought which in real life situations implies the purchasing of 13 pairs.

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 Exercises 73-80, solve each equation by the method of your choice. \(\frac{3 x^{2}}{4}-\frac{5 x}{2}-2=0\)

Use FOIL to find the products. \((2 x-1)(x+2)\)

Solve the quadratic equations by factoring. \(x^{2}-12 x=-36\)

The radicand of the quadratic formula, \(b^{2}-4 a c\), can be used to determine whether \(a x^{2}+b x+c=0\) has solutions that are rational, irrational, or not real numbers. Explain how this works. Is it possible to determine the kinds of answers that one will obtain to a quadratic equation without actually solving the equation? Explain.

Solve the equations using the quadratic formula. \(x^{2}+5 x+2=0\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.