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?
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.