Question

How do you solve `(p-2)/5=p/8`?

Answer 1

`p=16/3`

Explanation:

`"if "a/b=c/d" than "a*d=b*c`

`(p-2)/5=p/8`

`8*(p-2)=5*p`

`8*p-8*2=5p`

`8p-16=5p`

`"add -5p to both sides of equation "`

`8p-5p-16=cancel(5p)-cancel(5p)`

`3p-16=0`

`"add +16 to both sides of equation."`

`3p-cancel(16)+cancel(1)6=16`

`3p=16`

`"divide both sides of equation by 3"`

`(cancel(3)p)/cancel(3)=16/3`

`p=16/3`

Answer 2

See the entire solution process below:

Explanation:

First, multiply each side of the equation by the lowest common denominator of the two fractions which is `color(red)(40)` to eliminate the fractions while keeping the equation balanced:

`color(red)(40) xx (p - 2)/5 = color(red)(40) xx p/8`

`cancel(color(red)(40))8 xx (p - 2)/color(red)(cancel(color(black)(5))) = cancel(color(red)(40))5 xx p/color(red)(cancel(color(black)(8)))`

`8(p - 2) = 5p`

Next, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(8)(p - 2) = 5p`

`(color(red)(8) xx p) - (color(red)(8) xx 2) = 5p`

`8p - 16 = 5p`

Then, add `color(red)(16)` and subtract `color(blue)(5p)` from each side of the equation to isolate the `p` term while keeping the equation balanced:

`-color(blue)(5p) + 8p - 16 + color(red)(16) = -color(blue)(5p) + 5p + color(red)(16)`

`(-color(blue)(5) + 8)p - 0 = 0 + 16`

`3p = 16`

Now, divide each side of the equation by `color(red)(3)` to solve for `p` while keeping the equation balanced:

`(3p)/color(red)(3) = 16/color(red)(3)`

`(color(red)(cancel(color(black)(3)))p)/cancel(color(red)(3)) = 16/3`

`p = 16/3`

Answer 3

`p=16/3`

Explanation:

Cross multiply

`(color(green)(p-2))/color(red)5=color(red)p/color(green)8`

`color(blue)8(p-2)=5p`

Distribute the `8` into `p-2`

`color(blue)8p-2(color(blue)8)=5p`

`8p-16=5p`

Subtract `5p` from both sides

`8pcolor(blue)(-5p)-16=cancel(5pcolor(blue)(-5p))`

`3p-16=0`

Add `16` to both sides

`3pcancel(-16color(blue)(+16))=0color(blue)(+16)`

`3p=16`

Divide both sides by 3

`(cancel3p)/cancelcolor(blue)3=16/color(blue)3`

`p=16/3`

This is the final answer (it cannot be simplified furthermore)