Question

Somebody please help me out! i’m struggling!

Answer 1

Explanation:

To find the values of x and y in the given equation, we can follow these steps:

Step 1: Rewrite the equations in the given form:

Plan 1: 12x + y = 54.50

Plan 2: 6x + y = 30.20

Step 2: Use the method of elimination to solve for x:

Subtract the second equation from the first equation:

(12x + y) - (6x + y) = 54.50 - 30.20

Simplify and combine like terms:

12x - 6x + y - y = 24.30

Simplify further:

6x = 24.30

Divide both sides of the equation by 6:

x = 24.30/6

Simplify:

x = 4.05

Step 3: Substitute the value of x into either equation to find y:

Let's use Plan 1:

12(4.05) + y = 54.50

Multiply:

48.60 + y = 54.50

Subtract 48.60 from both sides:

y = 54.50 - 48.60

Simplify:

y = 5.90

So, the solution to the system of equations is x = 4.05 and y = 5.90.

Answer 2

Cost per month = $4.05

Start-up fee = $5.90

Explanation:

To find the cost per month and the cost of the start-up fee (assuming that the start-up fee is the same for both plans), we can set-up and solve a system of equations.

Let x be the monthly cost (in dollars).

Let y be the start-up fee (in dollars).

Given that Plan 1 offers 12 months of streaming plus the start-up fee for $54.50, then the equation that expresses this is:

`12x + y = 54.50`

Given that Plan 2 offers 6 months of streaming plus the start-up fee for $30.20, then the equation that expresses this is:

`6x + y = 30.20`

Subtract the second equation from the first equation to eliminate y:

`\begin{array}{rcrcrl}&12x& +& y& =& 54.50\\-&(6x& +& y& =& 30.20)\\\cline{2-6}&6x&&&=&24.30\end{array}`

Solve for x:

`\begin{aligned}6x&=24.30\\\\(6x)/(6)&=(24.30)/(6)\\\\x&=4.05\end{aligned}`

Substitute the found value of x into one of the equations and solve for y:

`\begin{aligned}12(4.05) + y &= 54.50\\48.60+ y &= 54.50\\y &= 5.90\end{aligned}`

Therefore, the cost per month is $4.05 and the start-up fee is $5.90.

`\hrulefill`

Understand & Think

The problem wants us to figure out Liz's monthly and initial fees for signing up with a streaming service by comparing two plans: Plan 1 and Plan 2. Since Plan 2 is designed for a 6-month duration, if Liz extended it to 12 months, it would result in a higher cost compared to Plan 1, as she would effectively pay the start-up fee twice. Consequently, Plan 2 would cost $60.40 for 12 months, which is $5.90 more than Plan 1 for the same period.

Given that the price difference is relatively small at $5.90, it could be advisable for Liz to start with Plan 1 when trying out the streaming service. This way, she avoids committing to a 12-month subscription and retains flexibility in case she is dissatisfied with the service. Nevertheless, the plan Liz should choose depends on her personal finances and needs.