SOLUTION: Please help me answer this question on grpah and algebraically : You are comparing two mobile phone text plans that a phone company has to offer. Plan A: uses formula y= 0.07

Question 1188058: Please help me answer this question on grpah and algebraically :
You are comparing two mobile phone text plans that a phone company has to offer.
Plan A: uses formula y= 0.07x
Plan B: uses formula y=0.02x+10
Where y is the monthly cost, in pounds and x is the number of texts sent or received per month. Draw the horizontal axis for x from 0 to 240 and the vertical axis for y from 0.25
a) Draw the graph of y=0.07x
b) Draw the graph of y=0.02x+10
Use your graph to answer the following:
c) Which Plan is it cheaper to use if you were sending/receiving 10 texts per day?
d) Which Plan is it cheaper to use if you were sending/receiving 180 texts per month ?
e) for what number of texts do both plans make the same charge?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's my graph.

red is .07 pounds per text.
blue is .02 pounds per text plus 10 pounds for the month.

from the graph, you can see that the plans break even when the user sends 200 texts per month.

when that occurs, the cost is 14 pounds for the month.

if the number of texts per month is greater than 200, then the .02 pounds per text + 10 pounds per month is cheaper.

on the graph, y is the total cost per month and x is the number of texts per month.

there are approximately 365/12 = 30.4 days in a month.

at 10 texts a day, you would be sending approximately 10 * that = 304 texts for the month.

at a cost of .07 per text, that would be equal to .07 * 304 = 21.28 pounds for the month.

at a cost of .02 per text + 10 pounds per month, that would be equal to .02 * 304 + 10 = 16.08 pounds for the month.

the .02x + 10 plan is cheaper at 304 texts per month.

if you are sending 180 texts per month, then:

at a cost of .07 per text, your cost for the month would be .07 * 180 = 12.6 pounds for the month.

at a cost of .02 per text + 10 pounds per month, your cost for the month would be .02 * 180 + 10 = 13.6 pounds for the month.

the .07 per text is cheaper at 180 texts per month.

at 10 texts per day, the .02 pounds per text + 10 pounds per month plan is cheaper.
at 180 texts per month, the .07 pounds per text is cheaper.

the graph shows the following:

coordinate points on the graph are in (x,y) format.
x is the number of text messages.
y is the total cost in pounds.

the blue is the .07 pounds per text plan.
the red is the .02 pounds per text plus 10 pounds per month plan.

at 10 texts per day, the number of texts per month is approximately 304.
the .02 pounds per text plus 10 pounds per month is cheaper, because .07 * 304 = 21.28, while .02 * 304 + 10 = 16.08 pounds.

at 180 texts per month, the .07 pounds per text plan is cheaper, because .07 * 180 = 12.6, while .02 * 180 + 10 = 13.6.

both plans cost the same at 200 texts a month.

here's what the graph looks like.

let me know if you have any questions.

theo
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