MODELING LINEAR EQUATIONS

Here, we are going to see, how a real world situation can be written as a linear equation using variable for the unknown quantity.

Examples 1-4 : In each case, write the given situation as a linear equation.

Example 1 :

3 more than the product of 4 and an unknown number is 75.

Solution :

Let x be the unknown number.

4x + 3 = 75

Example 2 :

3 less than 5 times a number is 22

Solution :

Let y be the unknown number.

5y - 3 = 22

Example 3 :

Eight less than four times a number n is 48.

Solution :

4n - 8 = 48

Example 4 :

How many raisins are left in a jar of 37 raisins after you have eaten some?

Solution :

Let x be the number of raisin eaten and y be the number of raisins are left in the jar.

y = 37 - x

Example 5 :

The fare for riding in a taxi is a $2 fixed charge and $0.50 per mile. The fare for a ride of m miles is $13.40. Write a linear equation that could be used to find the value of m.

Solution :

2 + 0.50m = 13.40

Example 6 :

Enny was selling Girl Scout cookies for the local Girl Scout Troop. Each box of cookies cost $2.95. Mrs. Peter’s purchase of Girl Scout cookies totaled $14.75. Write a linear equation to determine how many boxes of Girl Scout cookies were purchased by Mrs. Peter.

Solution :

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

2.95x = 14.75

Example 7 :

The football team is having a fundraiser to buy new uniforms. Football bumper stickers cost the football team $2.00 each. The football team sells them for $4.75. Write a linear equation to determine the number of bumper stickers that must be sold for the football team to make a profit of $137.50?

Solution :

Let x be the number of bumper stickers purchased and sold to make a profit of $137.50.

4.75x - 2.00x = 137.50

Example 8 :

Mrs. Baker purchased a number of juice packs at a cost of $0.30 each and a loaf of bread that cost $1.19. The total cost of her purchases was $2.99. Write a linear equation to determine how many juice packs Mrs. Baker purchased.

Solution :

Let j be the number of number of juice packs purchased.

0.30j + 1.19 = 2.99

Example 9 :

Mr. and Mrs. Sogard borrowed $4,200 from a bank, so that they could purchase an automobile. The interest on the loan was $25 per month. They paid the loan back in three years with equal monthly payments. Write a linear equation that can be used to calculate p the Sogard’s monthly payment.

Solution :

Example 10 :

Michael charges a flat rate of $25 plus $20 per hour to service furnace and air conditioners. Write a linear equation to determine the total fee.

Solution :

Let x be the number of hours and y be the total fee.

y = 25 + 20x

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