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

• Jan 4th 2011, 01:35 AM
glovergooner
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.
• Jan 4th 2011, 01:57 AM
jgv115
Ok think about it this way.

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

Now you have work out the area of each individual area

Quote:

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

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

Quote:

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
\$\displaystyle A2 = (2+w) * (0.5* 2w) \$

Quote:

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
\$\displaystyle A3= (3+w) * (2w+1) \$

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

\$\displaystyle 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
• Jan 4th 2011, 03:14 AM
glovergooner
Fantastic, thank you so much. This is great.