480-mm pipe is cut into three pieces. the second piece is three times as long as the first. the third piece is four times as long as the second. how long is each piece?
To find the lengths of each piece, let's assign variables to represent their lengths.
Let's say the length of the first piece is "x" mm.
According to the problem, the second piece is three times as long as the first piece. So the length of the second piece would be 3x mm.
Similarly, the third piece is four times as long as the second piece. So the length of the third piece would be 4(3x) = 12x mm.
To find the values of "x", "3x", and "12x", we need to consider the fact that the three pieces together make up a total length of 480 mm.
So, we can create an equation: x + 3x + 12x = 480.
Adding the x terms together gives us 16x, so the equation becomes 16x = 480.
To solve for "x", we divide both sides of the equation by 16: x = 480 / 16 = 30.
Now that we know "x", we can find the lengths of the three pieces:
The length of the first piece is x = 30 mm.
The length of the second piece is 3x = 3 * 30 = 90 mm.
The length of the third piece is 12x = 12 * 30 = 360 mm.
Therefore, the lengths of the three pieces are 30 mm, 90 mm, and 360 mm, respectively.
x + 3x + 4*3x = 480
(1 + 3 + 12)x = 480
16 x = 480
x = 30
3x = 90
12x = 360