Question

How do you solve `\frac { 8} { 3} = \frac { m - 5} { m - 10}`?

Answer 1

`m=13`

Explanation:

`8/3=(m-5)/(m-10)`

Multiply both sides by `3(m-10)`.

`3(m-10)xx8/3=3(m-10)xx(m-5)/(m-10)`

`cancel3(m-10)xx8/cancel3=3cancel((m-10))xx(m-5)/cancel(m-10)`

`(m-10)xx8=3xx(m-5)`

Open the brackets and simplify.

`8m-80=3m-15`

Subtract `3m` from each side.

`8m-3m-80=3m-3m-15`

`5m-80=-15`

Add `80` to each side.

`5m+80-80=80-15`

`5m=65`

Divide both sides by `5`.

`(5m)/5=65/5`

`(cancel5m)/cancel5=(13cancel65)/(1cancel5)`

`m=13`

Answer 2

`m=13`

Refer to the explanation for the process.

Explanation:

Solve:

`8/3=(m-5)/(m-10)`

Cross multiply. Multiply the denominators by the numerators of the opposite fractions.

`(8(m-10))/(3(m-5))`

Expand.

`8m-80=3m-15`

Subtract `3m` from both sides.

`8m-80-3m=3m-3m-15`

Cancel `3m` on the right side.

`8m-80-3m=color(red)cancel(color(black)(3m))-color(red)cancel(color(black)(3m))-15`

Simplify.

`5m-80=-15`

Add `80` to both sides.

`5m-80+80=-15+80`

Cancel `80` on the left side.

`5m-color(red)cancel(color(black)(80))+color(red)cancel(color(black)(80))=-15+80`

Simplify.

`5m=65`

Divide both sides by `5`.

`(5m)/5=65/5`

Cancel `5` on the left side.

`(color(red)cancel(color(black)(5^1))m)/color(red)cancel(color(black)(5^1))=65/5`

Simplify.

`m=13`