Question

76.Real-World Applications

Answer 1

Answer:

For plan B to save money cell phone user need to send 6000 texts per month as $\frac{x}{y}$ expresses the average texts sent per month by cell phone user and its obtained value is 6000.

Step-by-step explanation:

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

Plan A: $15 per month and $2 for every 300 texts.

Plan B: $25 per month and $0.50 for every 100 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 6

In Plan A $15 per month and $2 for every 300 texts are costed so the cost of Plan $\mathrm{A}$ is given by following equation,

$A=15 y+\frac{2 x}{300}$

In Plan B $\ 25$ per month and $\ 0 \cdot 50$for every 100 texts are costed so the cost of Plan B is given by following equation,

$B=25 y+\frac{0 \cdot 50 x}{100}$

Step 2 of 6

Now comparing the obtained equations $A=15 y+\frac{2 x}{300}$

and $B=25 y+\frac{0 \cdot 50 x}{100}$

$15 y+\frac{2 x}{300}=25 y+\frac{0 \cdot 50 x}{100}$

Step 3 of 6

Subtract $15 y$ from both the sides of the obtained equation $15 y+\frac{2 x}{300}=25 y+\frac{0 \cdot 50 x}{100}$ and simplify using subtraction properties.

$\begin{aligned}&15 y+\frac{2 x}{300}-15 y=25 y-15 y+\frac{0.50 x}{100} \\&\frac{2 x}{300}=10 y+\frac{1 x}{200}\end{aligned}$

Step 4 of 6

Subtract $\frac{x}{200}$ from both the sides of the obtained equation $\frac{2 x}{300}=10 y+\frac{1 x}{200}$ and simplify using subtraction properties.

$\begin{aligned}&\frac{2 x}{300}-\frac{x}{200}=10 y+\frac{1 x}{200}-\frac{x}{200} \\&\frac{x}{600}=10 y\end{aligned}$

Step 5 of 6

Multiply both the sides of the obtained equation $\frac{x}{600}=10 y$ by 600 and simplify using multiplication properties.

$\begin{aligned}&\frac{x}{600} .600=10 y .600 \\&x=6000 y\end{aligned}$

Step 6 of 6

Divide both the sides of the obtained equation x=6000 by y and simplify using division properties. As $\frac{x}{y}$ expresses the average texts sent per month by cell phone user. So, for plan B to save money cell phone user need to send 6000 texts per month.

$\begin{aligned}&\frac{x}{y}=\frac{6000 y}{y} \\&\frac{x}{y}=6000\end{aligned}$