A, B and C in percent

Question

If A is 50% larger than C and B is 25% larger than C, then A is what % larger than B? I know the answer but I do not know why it is that as i do not understand how to reach it, I would be extremely happy if anyone could help:)

Answer 1

First, write out what they give you:

(1) A = 1.5*C

(2) B = 1.25*C

From (2), we see that $C = \frac{B}{1.25}$. Plug this into (1) to get:

$A = 1.5 * (\frac{B}{1.25}) = \left(\frac{1.5}{1.25}\right) B$

So after calculating $\frac{1.5}{1.25}$, you know how much bigger A is than B

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The key idea here is to understand how to write "50%" bigger" in mathematics. If A is 50% bigger than C then A is equal to C plus 50% of C. "50% of C" expressed in decimals is 0.5*C. So, we have:

A = C + 0.5*C = 1.5*C

Once you know how to do this, your question becomes straight-forward.