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QuestionA 15 cm15 \mathrm{~cm} wire is cut into two pieces. The longer piece is 5 cm5 \mathrm{~cm} longer than the shorter. Find the shorter piece's length.

Studdy Solution

STEP 1

Assumptions1. The total length of the wire is15 cm. . The wire is cut into two pieces.
3. The longer piece is5 cm longer than the shorter piece.

STEP 2

Let's denote the length of the shorter piece as xx (in cm). Then, the length of the longer piece is x+5x +5 (in cm).

STEP 3

The total length of the wire is the sum of the lengths of the two pieces. So, we can write the equationx+(x+5)=15x + (x +5) =15

STEP 4

implify the equation by combining like terms.
2x+=152x + =15

STEP 5

Subtract5 from both sides of the equation to isolate the term with xx.
2x=15−52x =15 -5

STEP 6

Calculate the right side of the equation.
2x=102x =10

STEP 7

Divide both sides of the equation by2 to solve for xx.
x=10/2x =10 /2

STEP 8

Calculate the value of xx.
x=10/2=5x =10 /2 =5The length of the shorter piece of wire is5 cm.

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