a 5 foot stick is cut so that one part is 2\3 of other. how long,on inches is the shorter segment?
Well, if the stick is 5 feet long, that's 60 inches. And if you cut it into two segments where one is 2/3 of the other, that means the longer segment is (2/3)*60 = 40 inches. So the shorter segment would be the remaining 20 inches. But hey, don't worry, even the shorter segment can still measure up to some good jokes!
To find the length of the shorter segment, we first need to find the length of the longer segment.
Let's assume the length of the longer segment is x inches.
According to the given statement, the longer segment is 2/3 of the shorter segment. Therefore, the shorter segment would be 3/3 (which simplifies to 1) minus 2/3 of the total length, which is x:
Shorter segment = 1 - (2/3)x
Since the total length of the stick is 5 feet, we need to convert it to inches:
Total length = 5 feet * 12 inches/foot = 60 inches
Now, we equate the length of the longer segment to the total length of the stick:
x = 60 inches
Substituting this value into the equation for the length of the shorter segment:
Shorter segment = 1 - (2/3)(60)
Shorter segment = 1 - (2/3)(60/1)
Shorter segment = 1 - 40
Shorter segment = 60 - 40
Shorter segment = 20 inches
Therefore, the shorter segment is 20 inches long.
To find the length of the shorter segment, we can start by setting up a proportion based on the given information.
Let's assume the length of the shorter segment is represented by "x" inches. Since the longer segment is 2/3 of the total length, the length of the longer segment can be represented as (2/3) * 60 inches (since 5 feet is equal to 60 inches).
So, the proportion can be set up as:
x / (2/3 * 60) = (1 - 2/3) / (2/3 * 60)
Simplifying the proportions, we get:
x / (2/3 * 60) = 1/3 / (2/3 * 60)
Now, cross multiply and solve for x:
x * (2/3 * 60) = (1/3) * (2/3 * 60)
x * 2 * 60 = 1/3 * 2 * 60
x * 120 = 40
Divide both sides by 120:
x = 40 / 120
x = 1/3
Therefore, the shorter segment is 1/3 of 60 inches, which equals 20 inches.
Let x be the length of the longer segment.
In inches, x + (2/3)x = 60
5x/3 = 60
x/3 = 12
x = 36
The shorter pieces is 24 inches long.