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Check it out!

2.1.1: Properties of Equality

In October, Sydney was incorrectly charged \$67.50 for 18 books. How much should she have been charged?

2.1.1: Properties of Equality

During the month of September, Sydney downloaded 22 books and was charged \$75.

Set up an equation to find the charge for each downloaded book over 10.

30 + (22 – 10)x = 75

Solve the equation.

30 + 12x = 75

Simplify the equation.

12x = 45

Divide both sides by 12.

x = 3.75

2.1.1: Properties of Equality

In October, Sydney was incorrectly charged \$67.50 for 18 books. How much should she have been charged?

Set up an equation to find the amount that Sydney should have been charged.

The cost for 10 books is \$30. Each book over 10 costs an additional \$3.75. The total correct cost is30 + 3.75(x– 10).

2.1.1: Properties of Equality

Total cost = 30 + 3.75(x – 10)

Total cost = 30 + 3.75(18– 10)

Substitute the number of books she ordered for x.

Total cost = 30 + 3.75(8)

Multiply.

Total cost = 30 + 30

Total cost = 60

The total amount Sydney should have been charged for 18 books is \$60.

2.1.1: Properties of Equality

Use the equation for total cost found earlier to determine the number of books Sydney downloaded.

Total cost = 30 + 3.75(x – 10)

101.25 = 30 + 3.75(x – 10)

Substitute the value for total cost.

101.25 = 30 + 3.75x – 37.5

Distribute 3.75 over (x – 10).

101.25 = 3.75x – 7.5

Combine like terms.

2.1.1: Properties of Equality

108.75 = 3.75x

Add 7.5 to both sides of the equation.

29 = x

Divide both sides of the equation by 3.75.