Question

Tom is making a rectangular garden. he decides to make the garden 30 ft long by 15 ft wide. Later, tom decides to keep the length of the garden the same but change the width. Do the area a and the width w have a direct variation.

Answer 1

Yes.  Changing the the word problem into a function, you get 30x=y.

30 = Fixed Length

x = width

y = area

No matter what width (x) you choose, the area (y) is going to be a multiple of 30 (the fixed length) because with two numbers being multiplied, if there is a fixed number that will always be the multiple and not the multiplier.  For example, 10 multiplied by every number 1-10 is going to be a multiple of 10.

10x1=10, 10x2=20, 10x3=30, etc

So if Tom chooses any of these widths (x) 5, 10, or 15, y (the area) will be a multiple of 30.

30(5)=150

30(10)=300

30(15)=450

So as we double 5 to get 10, our outcome is doubled 150 to 300 and so forth.  Hope this helps.