Question 10951: A piece of wooden rod 33 cm. long is to be divided into 3 parts, each of which parts is to be progressively longer than the next part by two whole centimeters unit. How long is each part?
Answer by kinupanda(9)   (Show Source):
You can put this solution on YOUR website! Let us start by defining a variable for the first piece of wood we want to cut out of the whole... we will call it x. So we have a piece of wood x centimeters long.
We know from the question that the second piece of wood must be 2 cm longer than the first, so we can define its length with the expression x+2.
Similarly, the third piece must be another 2 cm longer than the second, so its length is (x+2)+2 cm, which simplifies to (x+4) centimeters.
Also from the question, we know that the total length of all three pieces of wood must add up to 33 cm. So we take the expressions: x + (x+2) + (x+4) = 33.
Now, we solve for x. Simplifying the left side of the equation yields: 3x+6 = 33. Thus, subtracting by 6 on both sides, 3x = 27; and by dividing by 3 on both sides, x = 9.
Now, we take our solution for x and plug it back into our expressions. Thus, the first piece of wood is x = 9 cm, the second is x+2 = 11 cm, and the third is x+4 = 13 cm.
To verify, we just add the lengths of the three pieces together, and sure enough, 9 + 11 + 13 adds up to 33 cm.
|
|
|
