# High School Math : How to do word problems where one quantity is unknown

## Example Questions

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### Example Question #1 : How To Do Word Problems Where One Quantity Is Unknown

Sarah sells necklaces for  each. She sells  necklaces in a month at this price. If she applied a % discount to the price of her necklaces, she would sell an additional  necklaces in a month. How much additional money would Sarah make in sales if she sold her necklaces with the % discount for a month?

Possible Answers:

Correct answer:

Explanation:

To find how much additional money Sarah would make by applying the discount, find the difference between her earnings in a normal month and a month where the discount is applied. In a normal month, multiply the normal price by the normal quantity sold to find the normal earnings:

To find earnings at the discounted price, first calculate how much each necklace will cost with the % discount. To do this, subtract the amount discounted (calculated by percent as a fraction of  multiplied by the original price) from the original price.

If  necklaces are sold at the new discounted price of  each, multiply these together to find the total earnings with the discount.

Finally, subtract the earnings without the discount from the earnings with the discount to find the additional money made by applying the discount.

### Example Question #2 : How To Do Word Problems Where One Quantity Is Unknown

Rojo Salsa is on sale at a price of  for  jars of  ounces each. Verde Salsa is on sale at a price of  for  jars of  ounces each. Which of the following statements is true?

Possible Answers:

A jar of Verde Salsa costs more than a jar of Rojo Salsa.

An ounce of Rojo Salsa costs more than an ounce of Verde Salsa.

An ounce of Verde Salsa costs more than an ounce of Rojo Salsa.

Verde salsa sells at per ounce.

An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa.

Correct answer:

An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa.

Explanation:

The statement "A jar of Verde Salsa costs more than a jar of Rojo Salsa" can be tested by comparing the price per jar of each salsa.

versus

The statement is false since the price of Rojo per jar is greater.

The remaining statements above can all be proven true or false by finding the price per ounce of each salsa.

Rojo Salsa is on sale at a price of  for  jars of  ounces each. The following operations can be used to determine the cost of Rojo Salsa per ounce:

for Rojo Salsa.

Verde Salsa is on sale at a price of  for  jars of  ounces each. The following operations can be used to determine the cost of Verde Salsa per ounce.

for Verde Salsa.

The only true statement is "An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa."

### Example Question #3 : How To Do Word Problems Where One Quantity Is Unknown

Sally went shopping and bought two shirts. One shirt cost $15, and she paid a total of$27 for both shirts. What was the cost of the other shirt?

Possible Answers:

cannot be determined

Correct answer:

Explanation:

To solve this word problem, set up an algebraic equation, putting  in for the unknown value of the second shirt. The equation is  because we know the cost of the two shirts will total .

To solve for , subtract  from each side. This results in .

### Example Question #4 : How To Do Word Problems Where One Quantity Is Unknown

A shirt costs $12 after a 15% discount. What was the original price of the shirt? Possible Answers: Correct answer: Explanation: Convert 15% to a decimal. Let the original price equal . The discount will be 15% of . Subtracting the discount from the original price will equal the amount paid,$12.

Using this equation, we can solve for .

### Example Question #5 : How To Do Word Problems Where One Quantity Is Unknown

A farmer has  units of fence. If he uses this to build a square fence, what will be the length of each side?

Possible Answers:

Correct answer:

Explanation:

If this is a square fence, then each of the four sides will be equal.

The fence in question will become the perimeter of that square.

Since  when working with a square, for this problem .

### Example Question #6 : How To Do Word Problems Where One Quantity Is Unknown

The area of a rectangle is . How many whole  by  rectangles can fit inside of this larger rectangle?

Possible Answers:

Correct answer:

Explanation:

First we need to find the area of the smaller rectangle.

Now to find out how many can fit, we divide the total area by the smaller area.

However, the problem is asking how many WHOLE rectangles can fit. Therefore only  can fit.

### Example Question #7 : How To Do Word Problems Where One Quantity Is Unknown

40% of Eric's socks are black, and the rest are white. If he has 6 pairs of black socks, how many pairs of white socks does he have?

Possible Answers:

6

9

4

12

15

Correct answer:

9

Explanation:

First, use the information to find the total number of socks Eric has by setting up a proportion:

, where  is the number of total socks.

Once you cross multiply and divide, you will find that .

To find the number of white socks Eric has, subtract the number of black socks  from the total number of socks:

### Example Question #8 : How To Do Word Problems Where One Quantity Is Unknown

A chemistry student has of a acid solution.  She needs a acid solution for an experiement.  How much pure water should she add?

Possible Answers:

Correct answer:

Explanation:

pure water and pure acid

In general, mixture problems have the form:

, where volume and percent

The equation to solve becomes:

Then the solution is .

### Example Question #9 : How To Do Word Problems Where One Quantity Is Unknown

Sarah is having a birthday party.  She wants to invite friends.  Each invitation costs , and each stamp costs .  If she plans to mail all of the invitations, how much change should she get back if she pays with a bill?

Possible Answers:

Correct answer:

Explanation:

The cost of mailing each invitation is .

To invite everyone, it will cost .

Then the change is .

### Example Question #10 : How To Do Word Problems Where One Quantity Is Unknown

What number is of ?

Possible Answers:

Correct answer:

Explanation:

Look for the verbal cues in the question.  IS translates to "equals" and OF translates to multiplication.

Thus the equation to solve becomes:

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