On chatty cathy’s cell phone plan she pays for minutes used plus a fixed monthly charge. for 500 minutes she pays $35 total, and for 1500 minutes used she pays $55 total. what is her monthly fixed charge?

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On chatty cathy’s cell phone plan she pays for minutes used plus a fixed monthly charge. for 500 minutes she pays $35 total, and for 1500 minutes used she pays $55 total. what is her monthly fixed charge?

the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.

C) $25

Step-by-step explanation:

$25 is correct. The slope of the line from (35, 500) to 55, 1500) is 20/1000 = .02, which is her cost per minute. Plug in one of the points into the equation y = mx + b to find b, which is the fixed cost.

Hope this helps

-Amelia

Answer

Find out the what is her monthly fixed charge .

To prove

Let us assume that the cost per mintues = x

Let us assume that the monthly charge be = y

As given

n Chatty Cathy’s cell phone plan she pays for minutes used plus a fixed monthly charge.

For 500 minutes she pays $35 total

Than the equation becomes

500x + y = 35

As given

for 1500 minutes used she pays $55 total.

Than the equation becomes

1500x + y = 55

Subtracted 500x + y = 35 from 1500x + y = 55

1500x - 500x + y - y = 55 - 35

1000x = 20

[tex]x = \frac{20}{1000}[/tex]

x = $0.02

Put in the 500x + y = 35

500 × 0.02 + y = 35

10 + y = 35

y = 35 - 10

y = $25

Therefore the monthly fixed charge be $25.

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !

We are given : For 500 minutes she pays $35 total and for 1500 minutes used she pays $55 total.

So, we can put the given information in form of two coordinates :

( Number of minutes, Total amount).

(500, 35) and (1500, 55).

First we need to find the slope between those two coordinates.

[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(500,\:35\right),\:\left(x_2,\:y_2\right)=\left(1500,\:55\right)[/tex]

[tex]m=\frac{55-35}{1500-500}[/tex]

[tex]m=\frac{1}{50}[/tex]

Now applying slope-intercept form y=mx+b, where m is the slope and b is y-intercept.

y-intercept represents monthly fixed charge.

Plugging (x,y) = (500, 35) and slope m= 1/50 in slope-intercept form y=mx+b.

35 = 1/50 (500) +b

35 = 10 + b.

Subtracting 10 from both sides, we get

35-10 = 10-10 + b

b = 25.

Therefore, her monthly fixed charge is $25.

$25

Step-by-step explanation:

500 mins = $35 (fixed + per minute charge)

1500 mins = $55 (fixed + per minute charge)

If we let per minute charge be "m"

and

let fixed charge be "f"

we can write 2 equations as:

35 = 500m + f

and

55 = 1500m + f

Now,

We re-write both equations in terms of f and equate both expressions:

f = 35 - 500m

and

f = 55 - 1500m

Equating:

35 - 500m = 55 - 1500m

-500m + 1500m = 55 - 35

1000m = 20

m = 20/1000

m = 0.02

Now we find f, what we are looking for:

f = 35 - 500m

f = 35 - 500(0.02)

f = 25

So, the fixed charge is $25

Option 'C' is correct.

Step-by-step explanation:

Let the fixed monthly charges be x

Let the charges per minutes be y

According to question, we have

[tex]x+500y=\$35\\x+1500y=\$55[/tex]

Now, by using the method of substitution for solving the system of linear equation:

[tex]x=35-500y\\\\\text{ put in second equation i.e.}x+1500y=\$55\\\\35-500y+1500y=55\\\\35+1000y=55\\\\1000y=55-35\\\\1000y=20\\\\x=\frac{20}{1000}\\\\x=\frac{1}{50}[/tex]

Now, put the value of y in x , so we get,

[tex]x=35-500y\\\\x=35-500\times\frac{1}{50}\\\\x=35-10=\$25[/tex]

Hence, the monthly fixed charge is $25

Thus, Option 'C' is correct.