Respuesta :
Answer:
For plan B to save money cell phone user need to send 6000 texts per month as [tex]$\frac{x}{y}$[/tex] 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 $2 for every 300 texts are costed so the cost of Plan [tex]$\mathrm{A}$[/tex] is given by following equation,
[tex]$A=15 y+\frac{2 x}{300}$[/tex]
In Plan B [tex]$\$ 25$[/tex] per month and [tex]$\$ 0 \cdot 50$[/tex]for every 100 texts are costed so the cost of Plan B is given by following equation,
[tex]$B=25 y+\frac{0 \cdot 50 x}{100}$[/tex]
Step 2 of 6
Now comparing the obtained equations [tex]$A=15 y+\frac{2 x}{300}$[/tex]
and [tex]$B=25 y+\frac{0 \cdot 50 x}{100}$[/tex]
[tex]$15 y+\frac{2 x}{300}=25 y+\frac{0 \cdot 50 x}{100}$[/tex]
Step 3 of 6
Subtract $15 y$ from both the sides of the obtained equation [tex]$15 y+\frac{2 x}{300}=25 y+\frac{0 \cdot 50 x}{100}$[/tex] and simplify using subtraction properties.
[tex]$\begin{aligned}&15 y+\frac{2 x}{300}-15 y=25 y-15 y+\frac{0.50 x}{100} \\&\frac{2 x}{300}=10 y+\frac{1 x}{200}\end{aligned}$[/tex]
Step 4 of 6
Subtract [tex]$\frac{x}{200}$[/tex] from both the sides of the obtained equation [tex]$\frac{2 x}{300}=10 y+\frac{1 x}{200}$[/tex] and simplify using subtraction properties.
[tex]$\begin{aligned}&\frac{2 x}{300}-\frac{x}{200}=10 y+\frac{1 x}{200}-\frac{x}{200} \\&\frac{x}{600}=10 y\end{aligned}$[/tex]
Step 5 of 6
Multiply both the sides of the obtained equation [tex]$\frac{x}{600}=10 y$[/tex] by 600 and simplify using multiplication properties.
[tex]$\begin{aligned}&\frac{x}{600} .600=10 y .600 \\&x=6000 y\end{aligned}$[/tex]
Step 6 of 6
Divide both the sides of the obtained equation x=6000 by y and simplify using division properties. As [tex]\frac{x}{y}[/tex] 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.
[tex]$\begin{aligned}&\frac{x}{y}=\frac{6000 y}{y} \\&\frac{x}{y}=6000\end{aligned}$[/tex]
