# Given $a= 4bc,\ a =100,\ b=2$, work out the value of $c$

I've come up with 12.5 because that multiplied by 2 is 25 and 25 times 4 is a hundred.

Am I correct by doing this? Sorry if it's a stupid question.

• Yes, you are correct. Mar 7 '16 at 17:39
• Yes, you are correct - $c=12.5$. Notice that $\displaystyle a=4bc\implies c=\frac{a}{4b}=\frac{100}{4\times 2}=12.5$. Mar 7 '16 at 17:39
• Don't think that your question is stupid. Here is the place for math questions at any level. If you just show sufficient effort, then you will be welcome. Mar 7 '16 at 17:45
• It's not a stupid question. But how do work it out? Did you just try and guess until you found something that worked. Or did you work out with logic and algebra what it must be? [Placing a =100 and b = 2 into the first equation gives us 100 = 4*2* c. Do you see where to go from there?] Mar 7 '16 at 17:45
• i jus guessed to be honest with you
– greg
Mar 7 '16 at 17:53

$$100=4\cdot2c\Longleftrightarrow 100=8c\Longleftrightarrow c=\frac{100}{8}\Longleftrightarrow c=\frac{25}{2}$$

You have $a=4bc$ but immediately know $a=100$ and $b=2$. Substituting you get $$100=4(2)c$$ or $$100 = 8c$$ Divide both sides by 8 and you get the 12.5 you suggested $$\frac{25}{2}=c$$

$a\div 4b = c$

Now just substitute your values for $b$ and $c$ into the rearranged equation.