Pre-Algebra - Word Problems with One Unknown

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 = $112.50$

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:

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

The area of a circle is $A=9 \pi$ . Find its radius.

$\pi$

$3\pi$

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 area of a circle is found using the following formula: $A=\pi r^2$ .

$A=\pi r^2$

$9 \pi=\pi r^2$

Divide each side by pi $(\pi)$ .

$\frac{9 \pi}{\pi}=\frac{\pi r^2}{\pi}$

Take the square root of each side.

$\sqrt{r^2}=\sqrt{9}$

$r=\sqrt{9}$

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

Explanation

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

Take the cube root of each side. The cube root is the number that is multiplied by itself three times in order to equal the original number.

$\sqrt[3]{s^3}=\sqrt[3]{27}$

$s=\sqrt[3]{3*3*3}$

You go to the store and buy 9 bottles of water. You spend $11.25 for all. How much is each bottle of water?

Explanation

When you do not know the value of something, you assign it a variable. In this case, we do not know how much a bottle of water costs, so we will assign it a variable. We know we bought 9 bottles. We also know that our total cost is $11.25. So, we can set up the equation. We get

where x is the cost of a bottle of water. Now, we solve for x. We must divide both sides by 9. We get

$\frac{9x}{9} = \frac{$11.25}{9}$

Therefore, a bottle of water costs $1.25.

It costs $49 to rent a moving truck and it costs $0.75 per mile that you travel. Write the equation for the total cost of renting the truck and driving miles.

Explanation

When renting a truck, it doesn't matter if you drive 0 miles or 100 miles it will still cost you the rental charge. In this case it was $49. Every mile you drive it costs you $0.75. The cost for miles would be:

3 people can pave a driveway in 4 hours. How long will it take for 8 people to pave a driveway?

$1.5\ \text{hours}$

$2\ \text{hours}$

$32\ \text{hours}$

$2\frac{2}3\ \text{hours}$

$0.5\ \text{hours}$

Explanation

With inverse proportionality, when one quantity increases the other decreases, and vice versa. The key to solving this problem is to keep in mind that each person works at the same rate regardless of how many people share the workload.

Let:

= constant of proportionality (rate of work per person)

= time

= number of people

Using these variables, we can set up an equation that will give us the total time:

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

Solve for using the original information for 3 people.

$k=tn=(4)\times(3)=12$

Using this constant, we can return to the first equation and solve for the time when 8 people are working:

$t=\frac{k}{n}=\frac{12}8=\frac{3}2=1.5$

Michael plays basketball and makes more free throws than twice what Eli makes.

Together they make free throws.

How many does Eli make?

Explanation

Michael makes more than twice Eli.

If Eli makes then double that and add and that would be Michael's amount.

Eli makes free throws.

Create an equation to solve the scenario.

Megan needs dollars to buy a new pair of jeans. She received dollars from her grandmother for her birthday. Megan needs to figure out how much more she needs to save before she can buy the jeans.