a 17 foot piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
x + (2x+5) = 17
Calculate for x, then 2x+5.
3x=17-5
3x=12
x=12/3
x=4
FOR 2x+5
=2(4)+5
=8+5
=13
To find the lengths of both pieces, let's set up an equation.
Let's assume the length of the shorter piece is x feet.
According to the given information, the longer piece is 5 feet longer than twice the shorter piece. So, the length of the longer piece is 2x + 5 feet.
Since the total length of the string is 17 feet, we can write the equation:
Length of the shorter piece + Length of the longer piece = Total length of the string
x + (2x + 5) = 17
Now, we can solve this equation to find the value of x, which represents the length of the shorter piece.
Combine like terms:
3x + 5 = 17
Subtract 5 from both sides:
3x = 12
Divide both sides by 3:
x = 4
So, the length of the shorter piece is 4 feet.
Now, plug this value back into the expression for the longer piece:
Length of the longer piece = 2x + 5
Length of the longer piece = 2(4) + 5
Length of the longer piece = 8 + 5
Length of the longer piece = 13
Therefore, the lengths of both pieces are:
Shorter piece = 4 feet
Longer piece = 13 feet