How do you solve `3/5=12/(x+8)`?

Two fractions are equal if the product of the numerator of first and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second.

In other words, if you cross-multiply the numerators and denominators of the two fractions and end up with the same product, you can say that the two fractions are equal.

In this case, you have

`color(blue)(3)/color(purple)(5) = color(blue)(12)/color(purple)(x+8)`

Multiply the numerator of the first fraction by the denominator of the second fraction

`color(blue)(3) xx (color(purple)(x+8)) = 3x + 24`

Multiply the denominator of the first fraction and the numerator of the second fraction

`color(purple)(5) xx color(blue)(12) = 60`

The two fractions are equal if

`3x + 24 = 60`

Solve for `x` to find

`3x = 60 - 24`

`x = (60-24)/3 = 12`

Do a quick check to make sure that the calculations are correct

`3/5 = 12/(12 + 8)`

`3/5 = 12/20`

`3/5 = (color(red)(cancel(color(black)(4))) xx 3)/(color(red)(cancel(color(black)(4))) xx 5)" "color(green)(sqrt())`