# Pre-Algebra : Word Problems with One Unknown

## Example Questions

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### Example Question #1 : Word Problems With One Unknown

John makes $12.50/hour gardening. He earned$275 this week. Write the equation for figuring out his wages, and then solve it to find out how many hours he worked.

Explanation:

Step 1: In order to find out how many hours John works, you first need a formula for calculating his wages:

(hourly wage)(hours)= total wages

Step 2: substitute the known values (hourly wage, total wages)

Step 3: isolate the unknown variable (hours) by dividing both sides by his hourly wage, then solve

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 purchace fencing for the other sides. If she needs to fence in 225 meters2 for her dogs, and fencing costs $2.50 per foot of fencing, what will be the cost of fencing in this square play area? Possible Answers: Correct answer: 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: Find the square root of both sides to calculate the length of the base of the square All the sides are of equivilent length, so the total amount of fence required is: 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: ### Example Question #1 : Word Problems With One Unknown 3 people can pave a driveway in 4 hours. How long will it take for 8 people to pave a driveway? Possible Answers: Correct answer: 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: Solve for using the original information for 3 people. Using this constant, we can return to the first equation and solve for the time when 8 people are working: ### Example Question #1 : Word Problems 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? Possible Answers: Correct answer: 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: Using the information given: One hour is 60 minutes, so using the direct proportionality equation again gives: ### Example Question #1 : Algebraic Equations If it takes 9 hours for 4 people to build a shed, how many people are needed to build the same type of shed in one-third of the time? Possible Answers: Correct answer: Explanation: The constant of proportionality is equal to the product of time () and the number of people (). Let represent the time and number of people working on the first shed, and represent the time and number of people working on the second shed. Since is the same for both situations (it is a constant), we can set the first and second scenarios equal to each other. Now, this problem asks for the number of people needed to build the second shed. This means we need to find a way to solve for . We can divide both sides of our equation by : Use the given values to solve. Note that will be equal to 3 (one-third of the original 9). ### Example Question #1 : Algebraic Equations It takes 45 minutes to drive to the nearest bowling alley taking city streets going 30 miles per hour (mph). How long will it take to get there using the freeway going 65mph if the distance is the same? (Round to the nearest minute). Possible Answers: Correct answer: Explanation: We can set up a rate equation, in which distance is equal to rate (speed) times time: Our speed and time may change with the different routes, but the distance stays the same. City route: Freeway route: We can set these equations equal to each other, since both are equal to . Solve for the freeway time, , by rearranging and substituting the given values. Rounding to the nearest minute, we get 21 for our final answer. ### Example Question #1 : Word Problems 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:

### Example Question #1 : Word Problems With One Unknown

Grace is 4 years older than Elena. If Grace is 9 years old, how old is Elena?

Explanation:

Let Elena's be equal to :

### Example Question #1 : Algebraic Equations

Suzie needs to ride her bike to the grocery store, which is is 15 miles away. It takes Suzie 45 minutes to bike to the grocery store. What is Suzies average speed? Express answer in miles per hour.

Explanation:

Distance is the product of rate and time:

Plug in the information given in the problem, remembering that the questions says to state the answer in terms of miles per hour, and we are give her time in minutes. Change minutes to hours:

It took Suzie .75 hours to ride to the grocery store.

Suzie's rate is  .

### Example Question #2 : Word Problems With One Unknown

An ice cream cone costs  plus  sales tax. How many ice cream cones can be purchased for ?

Explanation:

Calculate the cost of an ice cream cone with tax:

Determine how many cones, , can be purchased for  by setting up the following equation:

Divide both sides by 3.18:

Therefore,  ice cream cones can be purchased for .

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