A support beam 15 m long is cut into two piece, the lengths of which are in the ratio of 2 to 3. What is the length of each piece?
Let x = the shorter piece.
2/5 = x/15
5x = 30
x = 6 m
Let's suppose the lengths of the two pieces are 2x and 3x.
According to the given information, the sum of the lengths of the two pieces is equal to the length of the support beam:
2x + 3x = 15
Combining like terms:
5x = 15
Dividing both sides of the equation by 5:
x = 3
Therefore, the length of the shorter piece is:
2x = 2 * 3 = 6 m
And the length of the longer piece is:
3x = 3 * 3 = 9 m
So, each piece is 6 m and 9 m long, respectively.
To find the length of each piece, we first need to determine the ratio between the lengths. We are given that the ratio of the lengths of the two pieces is 2 to 3.
Let's say the length of the first piece is 2x, and the length of the second piece is 3x. Therefore, the total length of the beam can be expressed as:
2x + 3x = 15
Combining like terms:
5x = 15
To isolate x and solve for it, we divide both sides of the equation by 5:
x = 15/5
x = 3
Now that we have the value of x, we can find the lengths of the two pieces:
Length of the first piece = 2x = 2(3) = 6 m
Length of the second piece = 3x = 3(3) = 9 m
So, the length of each piece is 6 meters and 9 meters, respectively.