# MODELING LINEAR EQUATIONS WORKSHEET

Problem 1 :

When 3 times of an unknown number is increased by 12, it results 34.

Problem 2 :

7 less than 6 times of an unknown number is 25.

Problem 3 :

3 less than the quotient of a number and 7 is 6.

Problem 4 :

How many cookies are left in a box of 58 cookies after you have eaten some?

Problem 5 :

The fare for hiring a taxi is a \$5 fixed charge and \$2 per mile. If the fare for a trip of m miles is \$75, write a linear equation that could be used to find the value of m.

Problem 6 :

Joe is selling cookies where each box of cookies costs \$3.25. Mr. Michael’s purchase of cookies totaled \$16.25. Write a linear equation to determine how many boxes of cookies were purchased by Mr. Michael.

Problem 7 :

A music team is having a fundraiser to buy new uniforms. Concert bumper stickers cost the music team \$3.00 each. The music team sells them for \$5.65. Write a linear equation to determine the number of bumper stickers that must be sold for the music team to make a profit of \$265?

Problem 8 :

To have a party at the sports club, you must pay \$50 plus \$5 per guest. Write a linear equation that relates the number of guests x to the cost of the party y.

Problem 9 :

Three years ago, you age was 2 times of your younger brother's age. Write an equation to solve for your brother’s present age in terms of your present age.

Problem 10 :

A person weighing 150 pounds walking at a rate of 2 mph burns about 4 calories/min. The same person can walk at a rate of 4.5 mph and burn about 7.3 calories/min. Write a linear equation to find the times a 150-lb person would need to walk at 2 mph and 4.5 mph in order to burn 300 calories.

## Answers

1. Answer :

Let x be the unknown number.

3x + 12 = 34

2. Answer :

Let y be the unknown number.

6y - 7 = 25

3. Answer :

4. Answer :

Let x be the number of cookies eaten and y be the number of cookies are left in the box.

y = 37 - x

5. Answer :

5 + 2m = 75

﻿6. Answer :﻿

Let x be the number of boxes of cookies purchased by Mr. Peter.

3.25x = 16.25

7. Answer :

Let x be the number of bumper stickers purchased and sold to make a profit of \$265.

5.65x - 3x = 265

8. Answer :

y = 50 + 5x

9. Answer :

Let x be the present age of mine and y be the present age of my younger brother.

y - 3 = 2(x - 3)

y = 2(x - 3) + 3

10. Answer :

Let x be the number of minutes the person walks at 2 mph and y be the number of minutes he walks at 4.5 mph in order to burn 300 calories.

Given : When he walks at 2 mph, he burns 4 calories/min and that of 7.3 calories/min at 4.5 mph.

4x + 7.3y = 300

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