# Thread: ratio and proportions

1. ## ratio and proportions

w/5=7/10 solve for w

2. Originally Posted by abner80
w/5=7/10 solve for w
In a proportion written: $\displaystyle w:5 :: 7:10$, the product of the extremes (the 1st and 4th terms) = the product of the means (the 2nd and 3rd terms). Knowing this, then

$\displaystyle \frac{w}{5}=\frac{7}{10}$

$\displaystyle 10w=35$

$\displaystyle w=\frac{35}{10}=\frac{7}{2}$

3. Try to get all variables (letters) on one side, numbers on the other. Your problem is that the answer, w, is divided by 5 on the lhs. You must do the opposite (ie multiply by 5) throughout the expression (do it on both sides) to remove the offending 5 and hence get w = ....

So

$\displaystyle \frac{w}{5}= \frac{7}{10}$

Multiply both sides by 5

$\displaystyle 5\times\frac{w}{5}= 5\times\frac{7}{10}$

Do some cancellation on lhs and tidying up on rhs

$\displaystyle w=\frac{7}{2} = 3.5$.

Hope that helps.