# Math Help - Setting up a quadratic equation from a worded question...

1. ## Setting up a quadratic equation from a worded question...

Hi, not sure whether this is Pre-uni or uni mathematics but any help would be greatly appreciated. The question states:

"The canteen in the Davis Road building occupies a total floor space of 12000m2. It is to be redeveloped into three separate areas. Area 1 will be self service. Its length will be twice its width. Area 2 will be table service. Its width will be 2m more than the width of Area 1 but its length will be half the length of Area 1. Area 3 will be academic staff only. Its width will be 1m more than the width of Area 2 and its length will be 1m more than the length of Area 1. Set up an appropriate quadratic equation, and use to calculate the width and length of Area 1, Area 2 and Area 3. Show all steps in your calculation clearly."

Could anyone please help me with an explanantion of how to go about completing this question? I don't even know where to start...

Thank you.

2. Ok think about it this way.

$A1+A2+A3 = 12000$ So all the individual areas add up to the grand total area of $12000m^2$

Now you have work out the area of each individual area

Area 1 will be self service. Its length will be twice its width.
We know that $A= l*w$

So in this case $A1=2w*w$

Area 2 will be table service. Its width will be 2m more than the width of Area 1 but its length will be half the length of Area 1
$A2 = (2+w) * (0.5* 2w)$

Area 3 will be academic staff only. Its width will be 1m more than the width of Area 2 and its length will be 1m more than the length of Area 1
$A3= (3+w) * (2w+1)$

Now sub all those individual equations back into equation 1 and solve for w

$12000 = 2w^2 + (2+w)(w) + (3+w)(2w+1)$

I leave you to do the rest. You have to expand then either factorise or use the quadratic formula

3. Fantastic, thank you so much. This is great.