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Sarah is building a fence for her dog's square play area. To reduce the cost, she is using her house as 1 side of the play area, meaning she only has to purchase fencing for the other sides. If she needs to fence in 225 meters2 for her dogs, and fencing costs $2.50 per meter of fencing, what will be the cost of fencing in this square play area?

$\small \small \$ 112.50$

$\small \$ 562.50$

$\small \$ 140.63$

$\small \$ 45$

$\small \$75$

Explanation

The first step is to figure out the perimeter of the square play yard with an area of 225 meters, first using the fomula:

$\small (area) = (base)^2$

Find the square root of both sides to calculate the length of the base of the square

$\small \small \small \small \sqrt225 = (base) = 15$

All the sides are of equivilent length, so the total amount of fence required is:

$\small \small (15)*3 = 45$

One side is "fenced" by the house, so that fenching does not need to be paid for. Thus, only the remaining 3 sides need to be paid for.

Finally, multiply the length of fencing needs by the cost of fence per foot to find your answer:

$\small 45 * $2.50 = $112.50$

$\small \small \$ 112.50$

$\small \$ 562.50$

$\small \$ 140.63$

$\small \$ 45$

$\small \$75$

Explanation

The first step is to figure out the perimeter of the square play yard with an area of 225 meters, first using the fomula:

$\small (area) = (base)^2$

Find the square root of both sides to calculate the length of the base of the square

$\small \small \small \small \sqrt225 = (base) = 15$

All the sides are of equivilent length, so the total amount of fence required is:

$\small \small (15)*3 = 45$

One side is "fenced" by the house, so that fenching does not need to be paid for. Thus, only the remaining 3 sides need to be paid for.

Finally, multiply the length of fencing needs by the cost of fence per foot to find your answer:

$\small 45 * $2.50 = $112.50$

While reading a book Sarah notices that she has read 3 pages after 10 minutes. If she keeps reading at this rate, how many pages will she have read in 1 hour?

$18\ \text{pages}$

$60\ \text{pages}$

$30\ \text{pages}$

$12\ \text{pages}$

$6\ \text{pages}$

Explanation

The number of pages read is directly proportional to the time spent reading. To solve this problem we need to find the constant of proportionality, which is represented by in the following relation:

Here is the number of pages read, and is time. Rearrange to solve for the constant:

$k=\frac{p}t{}$

Using the information given:

$k=\frac{3\ \text{pages}}{10\ \text{minutes}}$

One hour is 60 minutes, so using the direct proportionality equation again gives:

$p=\frac{3\ \text{pages}}{10\ \text{minutes}}\cdot 60=\frac{180\ \text{pages}}{10\ \text{hour}}=18$

While reading a book Sarah notices that she has read 3 pages after 10 minutes. If she keeps reading at this rate, how many pages will she have read in 1 hour?

$18\ \text{pages}$

$60\ \text{pages}$

$30\ \text{pages}$

$12\ \text{pages}$

$6\ \text{pages}$

Explanation

The number of pages read is directly proportional to the time spent reading. To solve this problem we need to find the constant of proportionality, which is represented by in the following relation:

Here is the number of pages read, and is time. Rearrange to solve for the constant:

$k=\frac{p}t{}$

Using the information given:

$k=\frac{3\ \text{pages}}{10\ \text{minutes}}$

One hour is 60 minutes, so using the direct proportionality equation again gives:

$p=\frac{3\ \text{pages}}{10\ \text{minutes}}\cdot 60=\frac{180\ \text{pages}}{10\ \text{hour}}=18$

A father is buying cheeseburgers for his children. Each cheeseburger costs $3.50. He spends $17.50 on cheeseburgers. How many cheeseburgers did he buy?

Explanation

Set up and equation where is equal to the number of cheeseburgers:

Solve for c:

$\frac{17.50}{3.50}=\frac{3.50c}{3.50}$

A father is buying cheeseburgers for his children. Each cheeseburger costs $3.50. He spends $17.50 on cheeseburgers. How many cheeseburgers did he buy?

Explanation

Set up and equation where is equal to the number of cheeseburgers:

Solve for c:

$\frac{17.50}{3.50}=\frac{3.50c}{3.50}$

The volume of a cube is . Find the length of one of its sides.

Explanation

In order to solve this word problem, you have to know the correct geometric equation that is related to it. At that point, you can plug numbers of known values into the equation and solve it by reversing the operations performed on either side of the equals sign until the unknown variable is isolated and defined.

The volume of a cube is found using the following formula: .