how to answer this question? percentage increases

thank you for the answers received

i've attempted the method in the reply above but for some reason, i still don't fully understand how to work out the answer and obtain 44%. it's just not going into my mind!

I'll give you the details in this instance.

Lets start with:

$\displaystyle \frac{abc}{2d}+\frac{3bcd}{a+b+c}$

Each variable is increased by 20%, which is equivalant to multiplying it by 1.2.

So, our new formula is:

$\displaystyle \frac{(1.2)a(1.2)b(1.2)c}{2(1.2)d}+\frac{3(1.2)b(1.2)c(1.2)d}{(1.2)a+(1.2)b+(1.2)c}$

We can cancel 1.2 in the numerator and denominator of each to get.


$\displaystyle \frac{a(1.2)b(1.2)c}{2d}+\frac{3b(1.2)c(1.2)d}{a+b+c}$

And now pull out the common factor from each, giving.

$\displaystyle (1.2)^2\left[\frac{abc}{2d}+\frac{3bcd}{a+b+c}\right]$

So, our new value is (1.2)^2 = 1.44 times our old value, or an increase of 44%.