Q38. Crafts You make a decorative pap... [FREE SOLUTION]

91影视

Pre-algebra

Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

$Math Studyset 91影视 Explanations$ Math

Common Core Edition 路 183 pages

ISBN: 9780547587776

Chapter 2: Q38. (page 87)

Crafts You make a decorative paper chain with n links by cutting a 9 inch by 12 inch sheet of construction paper into n strips.
a. Write an expression in terms of n for the width of each paper strip.
b. Suppose you want each strip to be 0.75 inch wide. Use the problem solving strategy guess, check, and revise to find the number of links your paper chain will have.

Short Answer

Expert verified

The expression is $w = \frac{9}{n}$ .
The number of strips is $12$

Step by step solution

Apply the concept of equation:

An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement.

Example: 3x + 5 = 14 is an equation, in which 3x+5 and 14 are two expressions separated by an 鈥樷€檈qual鈥欌€� sign.

What are the steps to solve an equation?

Step 1: Simplify each side of the equation by removing parenthesis and combining the like terms.

Step 2: Use addition or subtraction to isolate the variable term on one side (preferably in the left side).

Step 3: Use Multiplication or Division to solve for the variable.

Write an expression in terms of n for the width of each paper strip.

A sheet of paper with lengthinchand width 9inch needs to cut into n strips.

Let the strips of each width $= w$ inch

As per the question: there are n strips covering with 9 inch.

So, we can write the equation: $w = \frac{9}{n}$

Apply the concept of equation:

An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement.

Example: 3x + 5 = 14 is an equation, in which 3x+5 and 14 are two expressions separated by an 鈥樷€檈qual鈥欌€� sign.

What are the steps to solve an equation?

Step 1: Simplify each side of the equation by removing parenthesis and combining the like terms.

Step 2: Use addition or subtraction to isolate the variable term on one side (preferably in the left side).

Step 3: Use Multiplication or Division to solve for the variable.

Use the problem solving strategy guess, check, and revise to find the number of links your paper chain will have.

A sheet of paper with lengthinchand width 9inch needs to cut into n strips.

Let the strips of each width $= w$ inch

As per the question: there are n strips covering with9 inch.

So, we can write the equation: $w = \frac{9}{n}$

Width of the strip is 0.75 inch.

Using the formula: $w = \frac{9}{n}$ and $w = 0.75$

$\begin{array}{l} w 鈥夆赌� = 鈥夆赌� \frac{9}{n} \\ 0.75 = \frac{9}{n} 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€� [鈥夆赌塖ubstitute鈥夆赌� w = 0.75 鈥夆赌�] \\ n 鈥夆赌� 路鈥夆赌� 0.75 鈥夆赌� = 鈥夆赌� n 鈥夆赌� 路鈥夆赌� \frac{9}{n} 鈥夆赌夆€夆赌� [鈥夆赌塎ultiply鈥夆赌塭ach鈥夆赌塻ide鈥夆赌塨y鈥夆赌� n 鈥夆赌�] \\ 0.75 鈥夆赌� n 鈥夆赌� = 鈥夆赌� 9 鈥夆赌� \\ \frac{0.75 鈥夆赌� n}{0.75} 鈥夆赌� = 鈥夆赌� \frac{9}{0.75} 鈥夆赌夆€� [鈥夆赌塂ivide鈥夆赌塭ach鈥夆赌塻ide鈥夆赌塨y鈥夆赌� 0.75 鈥夆赌�] \\ n = 鈥夆赌� \frac{9}{0.75} 鈥夆赌� = \frac{900}{75} \\ n 鈥夆赌� = 12 \end{array}$