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Company A charges $20.40 monthly for up to 3 gigabytes of data and $9.80 per additional gigabyte. Company B charges $18.60 monthly for up to 3 gigabytes of data and $10.10 per additional gigabyte. For what number of additional gigabytes would the two companies charge the same amount?

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Sprnt

Answer:

6 additional gigabytes. The price is $79.2 per month.

Step-by-step explanation:

To solve this problem, let's create a system of linear equations and solve it.

1. Create the equation ofCompany A.

This equation will give us the price that a service has based on the amount of gigabytes that a requested plan has.

[tex]C_A(g)=9.80g+20.40[/tex]; where g is the amount of gigabytes that a requested plan has

2. Create the equation of Company B.

Using the same as for Company A, Companie B's equation is the following:

[tex]C_B(g)=10.10g+18.60[/tex]

3. Write both equations in terms of "x" and "y".

[tex]y=9.80x+20.40\\\\y=10.10x+18.60[/tex]

4. Equal the right side of both equations.

[tex]9.80x+20.40=10.10x+18.60[/tex]

5. Substract 20.40 from both sides.

[tex]9.80x+20.40-20.40=10.10x+18.60-20.40\\ \\9.80x=10.10x-1.8[/tex]

6. Substract 10.10x from both sides.

[tex]9.80x-10.10x=10.10x-10.10x-1.8\\ \\-0.3x=-1.8[/tex]

7. Divide both sides by -0.3.

[tex]\frac{-0.3x}{-0.3} =\frac{-1.8}{-0.3} \\ \\x=6[/tex]

8. Conclude.

Taking into account that we formed a system of equations with equations that give the price of a services based on the number of additional, the number of additional gigabytes that make the price be the same is the solution of x for said system, which is x= 6.

9. (Extra) What would be the price?

To find out this information, just substitute the value of x= 6 into any of the equations and calculate the price:

[tex]C_B(6)=10.10(6)+18.60=79.2[/tex]

Hence, the price is $79.2 per month.

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semsee45

Answer:

6 additional gigabytes

Step-by-step explanation:

Given information:

  • Company A charges $20.40 monthly for up to 3 gigabytes of data and $9.80 per additional gigabyte.
  • Company B charges $18.60 monthly for up to 3 gigabytes of data and $10.10 per additional gigabyte.

Define the variables:

  • Let x = number of additional gigabytes of data.
  • Let y = total charge (in dollars).

Create two equations with the given information and the defined variables:

[tex]\begin{cases}\textsf{Company A:} \quad y=20.40+9.80x\\\textsf{Company B:} \quad y=18.60+10.10x\end{cases}[/tex]

To find the number of additional gigabytes for which the two companies would charge the same amount, substitute the second equation into the first equation and solve for x:

[tex]\begin{aligned}& \textsf{Substitute}: & 18.60+10.10x & = 20.40+9.80x\\\\& \textsf{Subtract 18.60 from both sides}: & 10.10x & = 1.80+9.80x\\\\& \textsf{Subtract 9.80}x \textsf{ from both sides}: & 0.30x & = 1.80\\\\& \textsf{Divide both sides by 0.30}: & x & = 6\end{aligned}[/tex]

Therefore, the two companies will charge the same amount for 6 additional gigabytes.

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