Digits, Grade 7, Volume 1, Homework Helper

8-4: Additional Problem Solving

Part 1

Example Comparing Linear Equations

An 8th grade class wants to hire a DJ for their end-of-the-year party.

A coordinate graph of a linear relationship.

table with 1 row and 3 columns , row1 column 1 ,

  • a. Which DJ charges the highest hourly rate?

  • b. Which equation(s) show a proportional relationship between the number of hours x and the total cost y?

  • c. If you only have $150 to spend, which DJ can you hire for the longest period of time?

Solution

  • a. The slope of each equation represents the costs per hour.

    table with 2 rows and 3 columns , row1 column 1 ,

    DJ A charges $20 per hour, DJ B charges $40 per hour, and DJ C charges $25 per hour. DJ B charges the most per hour.

  • b. Equations of the form y = mx show a proportional relationship between x and y. Only the equation y = 40x shows a proportional relationship between the number of hours and the total cost.

  • c. In each equation, y represents the total cost for x hours. You need to find the x-value that corresponds to a y-value of 150. Substitute 150 for y and solve for x.


End ofPage 297

Table of Contents

Digits, Grade 7, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Expressions, Equations, and Relationships Unit C: Measurement and Geometry Unit D: Proportionality English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties