bacali wrote:The figure above represents a square garden that is divided into 9 rectangular regions with indicated dimensions in meters. The shaded regions are planted with peas, and the unshaded regions are planted with tomatoes. If the sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes, what is the value of x?
A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5
We know that the whole region is a square. Therefore, the base is also 9. Instead of calling the unknown length x1, let's call it (6-x).
So, we know that:
Shaded = Unshaded
9 + 9 + 3x + 3x + 3(6-x) = 9 + 3x + 3(6-x) + 3(6-x)
18 + 6x + 18 - 3x = 9 + 3x + 18 - 3x + 18 - 3x
36 + 3x = 45 - 3x
6x = 9
x = 1.5
I concur that (C) is the right answer.
Note that this would have also been a great question for backsolving. Start by plugging in either (B) or (D), then decide if you need a bigger value for x or a smaller one, then plug in one more choice.
If we had started with x=2, we'd get 6-x = 4, so:
Shaded = Unshaded
9 + 9 + 6 + 6 + 12 = 9 + 12 + 12 + 6
42 = 39
Plugging in x=2, the unshaded regions were too big, so we need to decrease the value of x to help equalize. Eliminate (D) and (E), try:
(B) x = 1; 6-x = 5
9 + 9 + 3 + 3 + 15 = 9 + 15 + 15 + 3
39 = 42
Now we've gone too far in the other direction: eliminate (A) and (B), choose (C), the only option remaining.
