An online bookstore offers two subscription options for downloading e-books. Store A charg… — ACT

An online bookstore offers two subscription options for downloading e-books. Store A charges a monthly membership fee of $6.00$ plus $1.25$ per e-book download. Store B has no membership fee and charges $2.75$ per e-book download. A customer downloads the same number of e-books from each store in a single month and spends a total of $46.00$ across both stores. How many e-books did the customer download from each store?

A
4
B
7
10Answer
D
11.5
E
13

Answer

10 e-books from each store

The correct answer represents the number of downloads from each store that satisfies the total cost equation. Let

x

represent the number of books downloaded from each store. The cost at Store A is

6.00 + 1.25x

and the cost at Store B is

2.75x

. Since the total spent is

46.00

, we write the equation

(6.00 + 1.25x) + 2.75x = 46.00

. Combining like terms gives

6.00 + 4.00x = 46.00

. Subtracting

6.00

from both sides gives

4.00x = 40.00

, and dividing by

4.00

yields

x = 10

Step-by-Step Solution

Define the variable and write the expressions for the cost of each store.

Let

x

be the number of e-books downloaded from each store. Store A cost is

6.00 + 1.25x

, and Store B cost is

2.75x

Establishing algebraic expressions represents the verbal statements mathematically.

Set up the total cost equation by summing the costs of both stores and setting it equal to the total spent.

(6.00 + 1.25x) + 2.75x = 46.00

The customer spends a combined total of

46.00

across both bookstores.

Combine like terms and solve for the variable

x

6.00 + 4.00x = 46.00 \implies 4.00x = 40.00 \implies x = 10

Isolating the variable determines the number of e-books downloaded from each store.

Key Concept

Solving linear equations in one variable derived from real-world scenarios.

Estimated Time:1m 30s

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