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

Question

Hazel Anglin · Accepted Answer

#x = 12#

If the product of the first fraction's numerator and denominator equals the product of the first fraction's denominator and second fraction's numerator, then the two fractions are equal.

Put another way, you can say that two fractions are equal if you cross-multiply their numerators and denominators and get the same result.

Here, you've

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

Multiply the first fraction's numerator by the second fraction's denominator.

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

Multiply the first fraction's denominator by the second fraction's numerator.

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

If... then both fractions are equal.

#3x + 24 = 60#

Solve for #x# to find

#3x = 60 - 24#

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

Verify the calculations one last time to make sure they are accurate.

#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())#

Genesis Allen · Answer

undefined To solve the equation 3/5 = 12/(x + 8), cross multiply to get 3(x + 8) = 5 * 12. Simplify to get 3x + 24 = 60. Subtract 24 from both sides to get 3x = 36. Finally, divide by 3 to find x = 12.