Company A charges $25 per month plus $0.22 per minute for cell phone service. Company B charges $35 per month plus $0.12 per minute. How many minutes of usage is needed in one month to make Company B a better deal?
Company A charges $25 per month plus $0.22 per minute for cell phone service. Company B charges $35 per month plus $0.12 per minute. How many minutes of usage is needed in one month to make Company B a better deal?
You need to get the equation giving the total you have to pay for each company. There is a constant (monthly charge) in each of the two cases and a gradient (rate of call per minute).
Once you get the two equations, find where they intercept, that's where they cost the same. This will give you the amount of time one would have to pay the same fee in total for a certain amount of minutes. Before that point, one company charges more than another and beyond that point, the other company charges more than the previous.
Can you try that out?
Thats the problem I have I never know where to start and how to begin.
Okay, have you learned about linear equations?
It's in the form:
y = mx + c
This is the equation of a line on cartesian plane (coordinates system/grid)
where y is a variable (usually a dependent variable, if you don't know what that means, it's okay)
x is an independent variable (same here, but it's just like an opposite of y)
m is a gradient or slope and determines how fast the line climbs up or down.
c is a y-intercept, which means where the line meets the y-axis.
In your problem, you are given for company A giving $25 per month and a rate of $0.22 per minute of call. The $25 is a constant and you have to pay that amount regardless of how much time you spend on calls. The $0.22 is another constant. You will have to pay $0.22 for every additional minute you use, no more, no less. But what happens here is that the more you make calls, the larger the total amount will be.
This can be written as:
y = 0.22x + 25
Let's see. If you don't make any call, you will have to pay $25, right?
So, y = 0.22(0) + 25 = 0 + 25 = 25
What I did is understand that y gives the total money I have to pay if I make no call at all and x is the number of minutes I spend on calls. Similarly, having 1 minute of call means I have to pay $0.22 on top of $25, right?
y = 0.22(1) + 25 = $25.22
That's exactly it!
So, I can take any value of x in that equation and the resulting y that I calculate will give me the total fees I'll have to pay company A. Can you try to make the equation for company B?
y=0.12x+35
but how will we know how much minutes and which one is the better deal?
Okay, now the good thing about equations in general, is that you can manipulate them to give you things!
The first equation:
[tex]y_A = 0.22x + 25[/tex]
The second equation:
[tex]y_B = 0.12x + 35[/tex]
The first y gives you the total fee you have to pay to company A, right? (I added a small A to show that this is the amount received from company A) The second y gives you the total fee you have to pay to company B, right? So... when do the two companies charge the same fee? The answer is obtained by equating both equations!
Thus, we have:
[tex]y_A = y_B[/tex]
But what is yA and yB?
[tex]0.22x + 25 = 0.12x + 35[/tex]
Can you solve this equation for x?
25.22x=35.12x
I'm afraid not. You cannot add a number with a term in x.
For instance, you cannot do this:
2x + 3 = 5x
That is NOT true. Why? Take x to be at least two different numbers you want, take the left side. Let's suppose I take x = 0.
(2 * 0) + 3 = 3
On the right side:
5 * 0 = 0
Does 3 = 0?
Of course not!
If you repeat the same with 2 instead of 0, you would end up with 7 on the left side and 10 on the right side.
You can only add things with x with other things in x. Things without x cannot be added/subtracted to things without x.
Back to the equations now:
[tex]0.22x + 25 = 0.12x + 35[/tex]
On both sides of the equation, subtract 25 and post what you get.
0.22x+25=0.12x+35
-25 -25
------------------------------
0.22x=0.12x+10
Good! ^_^
Do you see what we're trying to do? Did you notice how one term in x on the left is now alone?
Now we need to remove the other term in x from the right side. So, subtract 0.12x from both sides.
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