Question

75. Real-World Applications

A cell phone company offers two plans for minutes. Plan A: $20 per month and $1 for every one hundred texts. Plan B: $50 per month with free unlimited texts. How many texts would you need to send per month for plan B to save you money?

Answer 1

t =amount of texts

a. 0.01t+20=y

b. 50=y

so that means that they equal each other

0.01t+20=50

-20

0.01t=30

t=3001

Hope This Helps!!!

Answer 2

For plan B to save money cell phone user need to send 3000 texts per month as
`(x)/(y)` expresses the average texts sent per month by cell phone user and its obtained value is 3000.

Explanation:

In the question it is given that a cell phone company offers two plans for minutes.

Plan A: $20 per month and $1 for every one hundred texts.

Plan B: $50 per month with free unlimited texts.

It is required to find that how many texts would be needed to send per month for plan B to save money. be needed to send per month for plan B to save money.

Step 1 of 5

In Plan A $20 per month and $1 for every one hundred texts are costed so the cost of Plan A is given by following equation,

`$A=20 y+(x)/(100)$`

In Plan B $50 per month with free unlimited texts are costed so the cost of Plan B is given by following equation,

`$$B=50 y$$`

Step 2 of 5

Now comparing the obtained equations
`$A=20 y+(x)/(100)$`

and B=50y.

`$20 y+(x)/(100)=50 y$$`

Step 3 of 5

Subtract 20y from both the sides of the obtained equation
`$20 y+(x)/(100)=50 y$` and simplify using subtraction properties.

`$$\begin{aligned}&20 y+(x)/(100)-20 y=50 y-20 y \\&(x)/(100)=30 y\end{aligned}$$`

Step 4 of 5

Multiply both the sides of the obtained equation
`$(x)/(100)=30 y$` by 100 and simplify using multiplication properties.

`$$\begin{aligned}&(x)/(100) \cdot 100=30 y .100 \\&x=3000 y\end{aligned}$$`

Step 5 of 5

Divide both the sides of the obtained equation x=3000y by y and simplify using division properties.

`$$\begin{aligned}&(x)/(y)=(3000 y)/(y) \\&(x)/(y)=3000\end{aligned}$$`

As
`$(x)/(y)$` expresses the average texts sent per month by cell phone user. So, for plan B to save money cell phone user need to send 3000 texts per month.