An online store sells two types of monthly subscription plans: a basic plan for 12 per mon… — SAT

An online store sells two types of monthly subscription plans: a basic plan for $12 per month and a premium plan for$ 20 per month. In April, the store had a total of 150 active subscribers for these two plans and collected a total of $2,280 in subscription fees. How many of the active subscribers in April were on the premium plan?

A
15
B
50
60Answer
D
90

Answer

By representing the number of basic subscribers as

x

and premium subscribers as

y

, we set up the system of equations

x + y = 150

and

12x + 20y = 2280

. Solving for

x

in the first equation gives

x = 150 - y

. Substituting this into the second equation yields

12(150 - y) + 20y = 2280

. Distributing the 12 and combining like terms gives

1800 + 8y = 2280

. Subtracting 1800 from both sides gives

8y = 480

, and dividing by 8 results in

y = 60

. Therefore, there were 60 premium subscribers.

Step-by-Step Solution

Define variables for the unknown quantities: let

x

represent the number of basic subscribers and let

y

represent the number of premium subscribers.

The system of equations is:

x + y = 150

and

12x + 20y = 2280

Translate the given information about total subscribers and total revenue into algebraic equations.

Express

x

in terms of

y

using the first equation (

x = 150 - y

) and substitute it into the second equation.

The substituted equation is:

12(150 - y) + 20y = 2280

, which expands to

1800 - 12y + 20y = 2280

Eliminate one variable to create a single equation with only one variable,

y

Simplify the equation and isolate

y

1800 + 8y = 2280 \implies 8y = 480 \implies y = 60

Combine like terms and use basic operations to solve for the number of premium subscribers.

Key Concept

Solving a system of two linear equations using substitution or elimination.

Estimated Time:1m 30s

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Step-by-Step Solution

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