mehdiov 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
You can use backsolving and a bit of logic to figure this one quickly:
We know that the garden is a square, with sides that are 9.
That means the Area of the Square is 81 meters squared.
We also know that the shaded region of peas is equal to unshaded regions of tomatoes;
So the area for each (peas and tomatoes) is 81/2 = 40.5
Off the bat we know that B and D can't be the answer (it has to be a non-integer number), BUT we can use B and D as test values as they're easier to work with.
B: 1
The shaded area the 2 boxes on the left side is 3 meters squared each (3*1) and the shaded area for the middlebox would be 15 (3*5).
The area of all of the shaded boxes would be (9+9+15+3+3) = 39, which is less than 40.5. That means A and B are out, so we need to test a bigger number.
D:2
The shaded area of the 2 boxes on the left side is 6 meters squared each (3*2) and the shaded area for the middlebox would be 12 (3*4).
The area of all of the shaded boxes would be (9+9+12+6+6) = 42, which is larger than 40.5. That means C has to be the answer!
The answer is C