if a wire 20 inches long is to be cut so that one piece is 2/5 as long as the other piece, how many inches long must the shorter piece be?
cut on L
the other is 2/5 L
so add them
7/5 L =20
L=100/7 inches=
and the shorter is 2/5 *100/7=40/7 inches
Well, well, well... cutting wires, huh? I hope you're not planning any mischief! Now, let me calculate the answer while I put on my imaginary wire-cutting hat... Ahem!
To solve this puzzle, we can create a little equation. Let's call the length of the shorter piece "x." According to your information, the longer piece will be 2/5 times the length of the shorter piece, so that makes it (2/5)x.
Now, since we know that the total wire length is 20 inches, we can add the lengths of the two pieces together and set it equal to 20:
x + (2/5)x = 20
Now, it's time for some algebra magic!
First, let's find a common denominator for that pesky fraction:
5x + 2x/5 = 20
After multiplying everything by 5, we get:
25x + 2x = 100
Combine like terms:
27x = 100
Now, let's isolate x by dividing both sides by 27:
x ≈ 3.70
So, the shorter piece should be around 3.70 inches long. But be careful! Keep your wires neat and don't let them tie you up in knots!
To solve this problem, we can set up and solve an equation.
Let's assume the length of the shorter piece is x inches. According to the problem, the longer piece must be 2/5 times the length of the shorter piece. Therefore, the length of the longer piece is (2/5)x inches.
The sum of the lengths of the two pieces is equal to the total length of the wire, which is 20 inches.
So, we can write the equation as follows:
x + (2/5)x = 20
To simplify this equation, we can multiply the whole equation by 5 to get rid of the fraction:
5x + 2x = 100
Combining like terms, we have:
7x = 100
Next, we can isolate x by dividing both sides of the equation by 7:
x = 100 / 7
By dividing 100 by 7, we get approximately 14.29.
Therefore, the shorter piece must be approximately 14.29 inches long.
To find the length of the shorter piece, we need to set up an equation based on the given information. Let's assume that the longer piece has a length of x inches and the shorter piece has a length of y inches.
According to the given information, the longer piece is 2/5 as long as the shorter piece. So, we can write the equation as:
x = (2/5)y
We also know that the total length of the wire is 20 inches. Thus, we can write another equation:
x + y = 20
Now we have a system of equations:
x = (2/5)y ...(Equation 1)
x + y = 20 ...(Equation 2)
To solve this system of equations, we can use the substitution method or elimination method. For simplicity, let's solve it using the substitution method.
First, substitute Equation 1 into Equation 2:
(2/5)y + y = 20
Multiply through by 5 to eliminate the fraction:
2y + 5y = 100
Combine like terms:
7y = 100
Divide both sides by 7:
y = 100/7
Therefore, the shorter piece should be approximately 14.29 inches long.