Question

I need help making a linear equation for this scenario?

"You have relatives living in the United Kingdom and in France. Suppose that you have purchased a prepaid phone card with a value of $75. Calls to the United Kingdom cost 23 cents per minute, while calls to France cost 21 cents per minute."

"Write a linear equation in two variables to represent the number of minutes you can use to call those two locations."

Answer 1

I'm guessing the variable would be minutes (m)?

Answer 2

And then the next part of that question tells me to graph the inequality... so I'm making inequalities?

Answer 3

@phi can you help me maybe?

Answer 4

Calls to the United Kingdom cost 23 cents per minute
I would change that to 0.23 dollars per minute.

calls to France cost 21 cents per minute." (or 0.21 dollars per minute)

It is true you want to keep track of minutes, but it makes a difference where you call.
How about minutes talking to the UK and minutes talking to France as the two variables.

Let's use x and y as the name of the variables (it will be easier to graph if we keep things x and y, because (maybe?) you know about graphing using x and y)

Can you pick what x will stand for? and what y will stand for ?

Answer 5

x will be minutes talking to UK and y will be minutes talking to France, is that alright?

Answer 6

yes, that is fine.

Next, if you talk x minutes (to the UK), how much does it cost ?

Answer 7

It costs 0.23x dollars to talk to the UK

Answer 8

yes, and how much does it cost to talk y minutes to France?

Answer 9

and then put them together... how much total does it cost to talk x minutes to the UK and y minutes to France ?

Answer 10

then, you make a relation, because you can only talk until your phone card with a value of $75 runs out of money.

in other words,

total cost of talking ≤ 75

Answer 11

Okay so 0.23x + 0.21y ≤ 75 ?

Answer 12

yes, exactly.

***And then the next part of that question tells me to graph the inequality***
for the moment, change the ≤ 75 to = 75
0.23x + 0.21y = 75
this is the equation of a line in standard form. There are a few ways to plot it.... use Geogebra (free software... see http://www.geogebra.org/cms/en/)

another way is set x =0, and solve for y:
0.23 * 0 + 0.21 y = 75
0.21 y = 75
divide both sides by 0.21 (calculator is helpful)
y = 75/0.21= 357 (rounded to the nearest minute)

that means (0, 357) is a point on the line.

now set y=0, and solve for x
you get
0.23 x = 75
x = 75/0.23 = 326

that means (326,0) is a point on the line.
Graph both points, and draw a straight line through them

Because the original relation has ≤ (as opposed to just <) , you make it a solid line
(it would be dashed if the relation was <)

Final step, shade the side of the line where the relation is true... below/left of the line should be shaded in.

Answer 13

I graphed it on desmos' graphing calculator (: It also says to "discuss a possible solution in the context of the real-life situation". I don't really understand what they mean by that.

Answer 14

Is there more background to that last part of the question?

Answer 15

Not really, that's all it says.

Answer 16

I can only guess what they want for
"discuss a possible solution in the context of the real-life situation"

But "a solution" means how many minutes you will talk to UK and to France.
One way to solve this is divide the money in half and spend $37.50 on each country.
Then figure out how many minutes that represents talking to the UK and how many minutes talking to France.

Answer 17

btw, here is what the graph looks like.
(Of course, we should exclude negative minutes for either country)

Answer 18

Oh okay, for the UK that would be about 163 minutes and for France it would be about 178 (I rounded both down because in this case I doubt you could round up as the prepaid time would probably not allow it)

Answer 19

yes, that makes sense.

Answer 20

Yay! Thank you very much for helping (:

Answer 21

yw