What is the height of the table? (SOLUTION)

We can solve this by doing some basic algebra. Let's first formulate the two scenarios:

1st equation: Height of Table (H) + Height of Cat (C) = 170 cm + Height of Turtle (T) = H + C = 170 + T

2nd equation: H + T = 130 cm + C

Subtract the 2nd equation from the first to eliminate H:

C - T = 40 + T - C.

Move over T and C to the left side to get:

2C - 2T = 40

Divide by 2:

C - T = 20

Now if we take the 2nd scenario equation and solve for H we get:

H = 130 + C - T = 130 + 20 = 150.

Thus, the height of the table is 150 cm.

BONUS: We solved for the height of the table without knowing the exact heights of the cat or table. If we plug in H = 150 cm into both equations we get:

150 + C = 170 + T or 150 + C - T = 170
150 + T = 130 + C or 150 - C + T = 130

There is no unique solution to these equations as what C and T can be any value so long as the difference C - T = 20.

For example, if the Cat was 1,000 cm, then the turtle has to be 980 cm.

Thus no, we can't solve for the height of the cat and turtle using this information alone.

Check out the puzzle (without the solution) by clicking here!

What is the height of the table? (SOLUTION)
View Comments