Question

How do you solve `6/10=(p-7)/(p+10)`?

Answer 1

The solution is `p=65/2`.

Explanation:

First, reduce the fraction:

`6/10=(p-7)/(p+10)`

`color(Red)cancelcolor(Black)6^3/color(red)cancelcolor(black)10^5=(p-7)/(p+10)`

`3/5=(p-7)/(p+10)`

Cross-multiply:

`3(p+10)=5(p-7)`

Use the distributive property:

`3*p+3*10=5*p-5*7`

`3p+30=5p-35`

`3p+30color(blue)+color(blue)35=5p-35color(blue)+color(blue)35`

`3p+30color(blue)+color(blue)35=5pcolor(red)cancelcolor(black)(color(black)-35color(blue)+color(blue)35)`

`3p+30color(blue)+color(blue)35=5p`

`3p+65=5p`

`3p+65color(blue)-color(blue)(3p)=5pcolor(blue)-color(blue)(3p)`

`color(red)cancelcolor(black)(3p)+65color(red)cancelcolor(blue)(color(blue)-color(blue)(3p))=5pcolor(blue)-color(blue)(3p)`

`65=5pcolor(blue)-color(blue)(3p)`

`65=2p`

`color(blue)(color(black)65/2)=color(blue)(color(black)(2p)/2)`

`color(blue)(color(black)65/2)=color(blue)(color(black)(color(red)cancelcolor(black)2p)/color(red)cancelcolor(blue)2)`

`color(blue)(color(black)65/2)=p`

This is the solution. Hope this helped!