An online bookstore charges a flat shipping fee plus a fixed price per book purchased. The… — SAT

An online bookstore charges a flat shipping fee plus a fixed price per book purchased. The total cost, $y$ , in dollars, for purchasing $x$ books is given by the equation $y = 8.5x + 4.5$ . If a customer's total cost was $47$ dollars, how many books did the customer purchase?

Answer: 5

Answer

The customer purchased 5 books.

To find the number of books purchased, substitute the total cost of 47 for

y

in the equation

y = 8.5x + 4.5

, yielding

47 = 8.5x + 4.5

. Subtracting

4.5

from both sides gives

42.5 = 8.5x

. Dividing both sides by

8.5

results in

x = 5

. Thus, the customer purchased 5 books.

Step-by-Step Solution

Substitute the total cost of 47 into the equation for y

47 = 8.5x + 4.5

Since the total cost is represented by y and is given as 47 dollars, we substitute 47 for y in the equation.

Subtract 4.5 from both sides of the equation

42.5 = 8.5x

Subtracting the flat fee from both sides isolates the variable term representing the total cost of the books.

Divide both sides by 8.5

x = 5

Dividing the remaining cost by the price per book yields the total number of books purchased.

Key Concept

Linear Equations in Two Variables

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