An online streaming service offers a basic monthly plan that costs 12 dollars plus 1.50 do… — ACT

An online streaming service offers a basic monthly plan that costs $12$ dollars plus $1.50$ dollars for each premium movie rented. A premium monthly plan costs $20$ dollars and includes $3$ free premium movie rentals, with each additional rental costing $1.00$ dollar. If a subscriber rents $x$ premium movies in a month, where $x > 3$ , which of the following expressions represents the savings, in dollars, of the premium plan compared to the basic plan?

A
$0.50x - 8$
B
$5 - 0.50x$
$0.50x - 5$ Answer
D
$2.50x - 11$
E
$0.50x - 11$

Answer

0.50x - 5

The cost of the basic plan for

x

rentals is

12 + 1.50x

dollars. Under the premium plan, the first

3

rentals are free, so the subscriber only pays for

x - 3

rentals. The cost of the premium plan is

20 + 1.00(x - 3)

dollars, which simplifies to

17 + x

dollars. The savings of the premium plan compared to the basic plan is the difference between the basic cost and the premium cost:

(12 + 1.50x) - (17 + x) = 0.50x - 5

dollars.

Step-by-Step Solution

Write the expression for the cost of the basic monthly plan.

12 + 1.50x

The basic plan has a flat fee of

12

dollars and a rate of

1.50

dollars per movie for all

x

movies rented.

Write the expression for the cost of the premium monthly plan.

20 + 1.00(x - 3)

, which simplifies to

17 + x

The premium plan has a flat fee of

20

dollars. Since

3

rentals are free, the subscriber only pays

1.00

dollar each for the remaining

x - 3

rentals.

Subtract the premium plan cost from the basic plan cost to find the savings.

(12 + 1.50x) - (17 + x) = 0.50x - 5

Savings represents the difference in cost: Basic Cost minus Premium Cost.

Key Concept

Translating verbal descriptions of multi-step costs into linear algebraic expressions and simplifying them.

Estimated Time:1m 30s

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