Ji-won joins a video streaming service that costs $30 per month. Three months later, he joins a music streaming service that costs $8 per month. Part A: Enter an equation that repr... Ji-won joins a video streaming service that costs $30 per month. Three months later, he joins a music streaming service that costs $8 per month. Part A: Enter an equation that represents the total cost in dollars for both services x months since joining the streaming service. Part B: If Ji-won has the video streaming service for 7 months, what is the total cost of both services?
Understand the Problem
The question is asking for an equation that calculates the total cost of a video streaming service and a music streaming service over a period of months. It includes two parts: the first part requires formulating the equation, and the second part requires calculating the total cost for a specific duration of one of the services.
Answer
The total cost for both services after 7 months is $242.
Answer for screen readers
The total cost after 7 months is $242.
Steps to Solve
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Understanding the services and costs Ji-won subscribes to a video streaming service costing $30 per month and a music streaming service costing $8 per month.
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Defining the total months of service Define ( x ) as the total number of months since Ji-won joined both services. Since Ji-won joins the music service 3 months after the video service, the relationship between the months for each service is:
- Video service: ( x ) months
- Music service: ( x - 3 ) months
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Formulating the total cost equation The total cost ( y ) after ( x ) months can be calculated as: $$ y = 30x + 8(x - 3) $$
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Simplifying the equation Distributing the payment for the music service: $$ y = 30x + 8x - 24 $$
Now combine like terms: $$ y = (30x + 8x) - 24 \ y = 38x - 24 $$
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Calculating the cost for 7 months To find the total cost for 7 months, substitute ( x = 7 ) into the total cost equation: $$ y = 38(7) - 24 $$
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Performing the calculations Calculating ( y ): $$ y = 266 - 24 \ y = 242 $$
The total cost after 7 months is $242.
More Information
Ji-won spends a total of $242 for both streaming services after enjoying the video service for 7 months and the music service for 4 months.
Tips
- Forgetting to account for the 3-month delay in the music service start date.
- Incorrectly calculating the number of months for each service, leading to an incorrect total cost.
- Not combining like terms properly in the equation.
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