The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone.

Question

The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 490 minutes, the monthly cost will be $273. If the customer uses 1000 minutes, the monthly cost will be $528.

A) Find an equation in the form y=mx+b,y=mx+b, where xx is the number of monthly minutes used and yy is the total monthly of the Splint plan.

Answer: y=y= 

 

B) Use your equation to find the total monthly cost if 617 minutes are used.

Answer: If 617 minutes are used, the total cost will be  dollars.

Answer 1

C= F + NM

where F= the monthly Fee, N = number of minutes used and M= the charge per minute

528= F + 1000M

273 =F + 490M

subtract

255 = 510M

M = 255/510 = 50 cents per minute = $0.50

F = 528 - 1000(.5) = 528-500 = $28 monthly Fee

C = 28 +N/2

C = 28 +617/2 = 28+303.50 = $331.50 for 617 minutes

Answer 2

Part A Solution:

With the information given in the problem, we know that (i) "if a customer uses 490 minutes, the monthly cost will be $273" and (ii) "if the customer uses 1000 minutes, the monthly cost will be $528."

From the information given in (i), we can set up the equation where y = total monthly payment = 273, x = minutes = 490, and where b = monthly fee which is an unknown value.

This gives the equation : y = mx+b --> 273 = 490m + b

*Note: m = the slope = rate, which can be defined as the $/min.

From the information given in (ii), we can set up the equation where y = total monthly payment = 528, x = minutes = 1000, and where b = monthly fee which is an unknown value.

This gives the equation: y = mx + b --> 528 = 1000m + b

At this point, we have two equations with two unknown values, m and b which are constant in both equations. The values that were given are the (x,y) values. To find the unknown m and b values, we can first use an equation to isolate one of the variables.

Solving for m:

From the first equation, b = 273 - 490m.

We can substitute this value of b into the second equation: 528 = 1000m + (273 - 490m)

Solve for m:

528 - 273 = 1000m - 490m

255 = 510m

m = 0.5

Solving for b:

From the first equation, since solving for m, we know that 273 = 490(0.5) + b

Now, we know that b = 273 - (490)0.5 = 28.

Answer for Part A: y = 0.5 x + 28

Part B Solution:

Using the equation y = 0.5 x + 28, we can substitute 617 minutes for x.

y = 0.5 (617) + 28

y = 336.5

Answer for Part B: If 617 minutes are used, the total cost will be $336.50.