Solved on Feb 02, 2024

Find the inequality for the number of copies you can make with $\$ 3.00$ if each copy costs $\$ 0.45$ , using $x$ as the variable.

STEP 1

Assumptions
1. You have $3.00 to spend on copies.<br />2. The cost per copy is$ 0.45.
3. You want to find the maximum number of copies you can make without exceeding the $3.00.<br />4. Use$ x$ to represent the number of copies.

STEP 2

To find the inequality that represents the number of copies you can make, you need to consider the total cost of $x$ copies. The total cost is the number of copies multiplied by the cost per copy.
$Total\, cost = Number\, of\, copies \times Cost\, per\, copy$

STEP 3

Now, express the total cost in terms of $x$ and the given cost per copy.
$Total\, cost = x \times \$0.45$

STEP 4

Since you cannot spend more than $3.00, the total cost must be less than or equal to$ 3.00. This gives us the inequality:
$x \times \$0.45 \leq \$3.00$

STEP 5

To find the maximum number of copies you can make, we need to solve the inequality for $x$ .
$x \leq \frac{\$3.00}{\$0.45}$

STEP 6

Now, divide $3.00 by$ 0.45 to find the maximum number of copies.
$x \leq \frac{\$3.00}{\$0.45}$

STEP 7

Calculate the value of $x$ .
$x \leq \frac{3}{0.45}$

STEP 8

Simplify the fraction to find the maximum number of copies.
$x \leq \frac{3}{0.45} = \frac{300}{45}$

STEP 9

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15.
$x \leq \frac{300 \div 15}{45 \div 15}$

STEP 10

Finish the calculation to find the value of $x$ .
$x \leq \frac{20}{3}$

STEP 11

Since you can't make a fraction of a copy, we need to find the greatest whole number of copies that is less than or equal to $\frac{20}{3}$ .
$x \leq 6$
The inequality that represents the number of copies you can make is:
$x \leq 6$
You can make at most 6 copies with $3.00 at a cost of$ 0.45 per copy.

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Find the inequality for the number of copies you can make with $\$ 3.00$ if each copy costs $\$ 0.45$ , using $x$ as the variable.

STEP 1

Assumptions
1. You have $3.00 to spend on copies.<br />2. The cost per copy is$ 0.45.
3. You want to find the maximum number of copies you can make without exceeding the $3.00.<br />4. Use$ x$ to represent the number of copies.

STEP 2

To find the inequality that represents the number of copies you can make, you need to consider the total cost of $x$ copies. The total cost is the number of copies multiplied by the cost per copy.
$Total\, cost = Number\, of\, copies \times Cost\, per\, copy$

STEP 3

Now, express the total cost in terms of $x$ and the given cost per copy.
$Total\, cost = x \times \$0.45$

STEP 4

Since you cannot spend more than $3.00, the total cost must be less than or equal to$ 3.00. This gives us the inequality:
$x \times \$0.45 \leq \$3.00$

STEP 5

To find the maximum number of copies you can make, we need to solve the inequality for $x$ .
$x \leq \frac{\$3.00}{\$0.45}$

STEP 6

Now, divide $3.00 by$ 0.45 to find the maximum number of copies.
$x \leq \frac{\$3.00}{\$0.45}$

STEP 7

Calculate the value of $x$ .
$x \leq \frac{3}{0.45}$

STEP 8

Simplify the fraction to find the maximum number of copies.
$x \leq \frac{3}{0.45} = \frac{300}{45}$

STEP 9

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15.
$x \leq \frac{300 \div 15}{45 \div 15}$

STEP 10

Finish the calculation to find the value of $x$ .
$x \leq \frac{20}{3}$

STEP 11

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Find the inequality for the number of copies you can make with $3.00\$ 3.00$3.00 if each copy costs $0.45\$ 0.45$0.45, using xxx as the variable.

STEP 1

STEP 2

STEP 3

Now, express the total cost in terms of xxx and the given cost per copy.Total cost=x×$0.45Total\, cost = x \times \$0.45Totalcost=x×$0.45

STEP 4

Since you cannot spend more than 3.00,thetotalcostmustbelessthanorequalto3.00, the total cost must be less than or equal to 3.00,thetotalcostmustbelessthanorequalto3.00. This gives us the inequality:x×$0.45≤$3.00x \times \$0.45 \leq \$3.00x×$0.45≤$3.00

STEP 5

To find the maximum number of copies you can make, we need to solve the inequality for xxx.x≤$3.00$0.45x \leq \frac{\$3.00}{\$0.45}x≤$0.45$3.00​

STEP 6

Now, divide 3.00by3.00 by 3.00by0.45 to find the maximum number of copies.x≤$3.00$0.45x \leq \frac{\$3.00}{\$0.45}x≤$0.45$3.00​

STEP 7

Calculate the value of xxx.x≤30.45x \leq \frac{3}{0.45}x≤0.453​

STEP 8

Simplify the fraction to find the maximum number of copies.x≤30.45=30045x \leq \frac{3}{0.45} = \frac{300}{45}x≤0.453​=45300​

STEP 9

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15.x≤300÷1545÷15x \leq \frac{300 \div 15}{45 \div 15}x≤45÷15300÷15​

STEP 10

Finish the calculation to find the value of xxx.x≤203x \leq \frac{20}{3}x≤320​

STEP 11

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Find the inequality for the number of copies you can make with $\$ 3.00$ if each copy costs $\$ 0.45$ , using $x$ as the variable.

Now, express the total cost in terms of $x$ and the given cost per copy.
$Total\, cost = x \times \$0.45$

Since you cannot spend more than $3.00, the total cost must be less than or equal to$ 3.00. This gives us the inequality:
$x \times \$0.45 \leq \$3.00$

To find the maximum number of copies you can make, we need to solve the inequality for $x$ .
$x \leq \frac{\$3.00}{\$0.45}$

Now, divide $3.00 by$ 0.45 to find the maximum number of copies.
$x \leq \frac{\$3.00}{\$0.45}$

Calculate the value of $x$ .
$x \leq \frac{3}{0.45}$

Simplify the fraction to find the maximum number of copies.
$x \leq \frac{3}{0.45} = \frac{300}{45}$

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15.
$x \leq \frac{300 \div 15}{45 \div 15}$

Finish the calculation to find the value of $x$ .
$x \leq \frac{20}{3}$