Question

Jacob cut a rectangular piece of wrapping paper to wrap his brother's gift. The piece of wrapping paper had a perimeter of 50 inches. The length was 5 less than the width. Write a system of equations to represent the situation and solve the system.

Answer 1

The length of wrapping paper piece is 10 inches and width is 15 inches.

Step-by-step explanation:

Let,

Length of rectangular piece = x

Width of rectangular piece = y

Perimeter = 50

2(x+y) = 50

Dividing both sides by 2

$\frac{2(x+y)}{2}=\frac{50}{2}\\x+y=25\ \ \ Eqn\ 1$

x+y=25   Eqn 1

The length was 5 less than the width.

x = y-5   Eqn 2

Putting value of x from Eqn 2 in Eqn 1

$(y-5)+y=25\\y-5+y=25\\2y=25+5\\2y=30$

Dividing both sides by 2

$\frac{2y}{2}=\frac{30}{2}\\y=15$

Putting y=15 in Eqn 2

$x=15-5\\x=10$

The length of wrapping paper piece is 10 inches and width is 15 inches.

Keywords: linear equation, substitution method

Learn more about substitution method at:

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