Question

problem 15
a garden plot has dimensions of 15 feet by 12 feet. if you want to enclose it with fencing at $8 per linear foot, what is the total cost?

problem 16
if 15% of a number is 45, what is the number?

problem 17
calculate: $\frac{3}{4} div \frac{1}{2}$

problem 18
a rope is $5\frac{1}{2}$ meters long. if you cut it into pieces that are $\frac{1}{2}$ meter long, how many pieces will you have?

problem 19
calculate: $\frac{2}{3} div \frac{4}{9}$

Explanation:

Problem 15

Step1: Find the perimeter of the garden plot.

The garden is a rectangle with length \( l = 15 \) feet and width \( w = 12 \) feet. The formula for the perimeter of a rectangle is \( P = 2(l + w) \).
Substituting the values, we get \( P = 2(15 + 12) = 2(27) = 54 \) feet.

Step2: Calculate the total cost.

The cost per linear foot is $8. So, the total cost is the perimeter multiplied by the cost per foot.
Total cost \( = 54 \times 8 = 432 \) dollars.

Step1: Let the number be \( x \).

We know that 15% of \( x \) is 45. Mathematically, this can be written as \( 0.15x = 45 \).

Step2: Solve for \( x \).

To find \( x \), we divide both sides of the equation by 0.15.
\( x=\frac{45}{0.15}=300 \).

Step1: Recall the rule for dividing fractions.

To divide two fractions \( \frac{a}{b}\div\frac{c}{d} \), we multiply the first fraction by the reciprocal of the second fraction, i.e., \( \frac{a}{b}\times\frac{d}{c} \).

Step2: Apply the rule to \( \frac{3}{4}\div\frac{1}{2} \).

The reciprocal of \( \frac{1}{2} \) is \( \frac{2}{1} \). So, \( \frac{3}{4}\div\frac{1}{2}=\frac{3}{4}\times\frac{2}{1} \).
Simplifying the multiplication, we get \( \frac{3\times2}{4\times1}=\frac{6}{4}=\frac{3}{2} \).

Answer:

The total cost is $432.

Problem 16