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QuestionA 9-foot ribbon is cut into two pieces, with one piece being 1 foot longer. Find the lengths of the pieces.

Studdy Solution

STEP 1

Assumptions1. The total length of the ribbon is9 feet. . The ribbon is cut into two pieces.
3. One piece is1 foot longer than the other piece.

STEP 2

Let's denote the length of the shorter piece as x (in feet). Therefore, the length of the longer piece is x +1.

STEP 3

According to the problem, the sum of the lengths of the two pieces is equal to the total length of the ribbon. We can express this as an equationx+(x+1)=9x + (x +1) =9

STEP 4

implify the equation by combining like terms.
2x+1=92x +1 =9

STEP 5

Next, we need to isolate the variable x. We can do this by subtracting1 from both sides of the equation.
2x=9−12x =9 -1

STEP 6

Calculate the right side of the equation.
2x=82x =8

STEP 7

Finally, to solve for x, we divide both sides of the equation by2.
x=/2x = /2

STEP 8

Calculate the value of x.
x=8/2=4x =8 /2 =4So, the length of the shorter piece is4 feet.

STEP 9

Now, we can find the length of the longer piece by adding to the length of the shorter piece.
Longer piece=x+Longer\, piece = x +

STEP 10

Plug in the value of x to calculate the length of the longer piece.
Longer piece=4+Longer\, piece =4 +

STEP 11

Calculate the length of the longer piece.
Longer piece=4+=5Longer\, piece =4 + =5So, the length of the longer piece is5 feet.
The lengths of the two pieces are4 feet and5 feet.

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