A 28-inch
board is to be cut into three pieces so that the second piece is
twicetwice
as long as the first piece and the third piece is
44
times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces
1st piece x=28
2nd piecex=28 squared which is 784
3rd piece 28 to the fourth power which is 3.77
what's all this power stuff?
1st piece = x
2nd piece = 2x
3rd piece = 4x
So, you have
x+2x+4x = 28
x = 4
A 20 inch board is 4 times to be cut into three pieces so that the second piece is as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
What is the length of the first piece?
To solve this problem, let's break it down step by step.
Step 1: Set up the equations
Let's assume the length of the first piece is x inches.
According to the problem,
The length of the second piece = 2 times the length of the first piece
= 2x inches.
The length of the third piece = 4 times the length of the first piece
= 4x inches.
Step 2: Set up the equation for the total length
We know that the total length of all three pieces is 28 inches, so we can write:
x + 2x + 4x = 28
Simplifying this equation, we get:
7x = 28
Step 3: Solve for x
To find the length of the first piece, we need to solve this equation for x.
Divide both sides of the equation by 7:
7x/7 = 28/7
x = 4
So, the length of the first piece (x) is 4 inches.
Step 4: Find the lengths of all three pieces
Now that we know the length of the first piece (x = 4), we can substitute this value into the equations from step 1 to find the lengths of the other two pieces.
Length of the second piece = 2x = 2 * 4 = 8 inches.
Length of the third piece = 4x = 4 * 4 = 16 inches.
Therefore, the lengths of all three pieces are:
First piece: 4 inches
Second piece: 8 inches
Third piece: 16 inches.
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