High School Math : How to do word problems where two quantities are unknown

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Do Word Problems Where Two Quantities Are Unknown

A farmer has  units of fence. If he uses this to build a square fence, what will be the area enclosed by the fence?

Possible Answers:

Correct answer:

Explanation:

Since we are looking at a square, the formula for the area of a square is .

Therefore we need to know the length of each side.

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

The amount of fence that the farmer has in the problem will become the perimeter of our square.

Since  when working with a square, for this problem .

Plug that into our original equation.

Example Question #2 : How To Do Word Problems Where Two Quantities Are Unknown

Rosie, Eileen and Sasha order a pizza. It is divided into  slices. Eileen eats  slice. Roseanne eats twice as many slices as Sasha.

If there are  slices of pizza remaining, how many slices did Sasha eat?

Possible Answers:

 slices

 slices

 slices

 slices

 slice

Correct answer:

 slices

Explanation:

Since the pizza began as  slices and there are now  slices remaining, a total of  slices were eaten (because ). Of the  eaten pieces, it is stated that  slice was eaten by Eileen. This means a total of  slices were eaten by Roseanne and Sasha combined. To find exactly how many slices Sasha ate, use the fact that Roseanne ate twice as many slices as Sasha. Write and solve for  in the following equation, where  is the number of slices Sasha ate. Note that  stands for the number of slices Roseanne ate, since she ate twice as many slices as Sasha.

 slices

Example Question #3 : How To Do Word Problems Where Two Quantities Are Unknown

A helicopter flies against the wind from city A to city B in 5 hours. The same helicopter returns from city B to city A, in the same direction as the wind, in 4 hours. Find the ratio of the speed of the helicopter to the speed of the wind. 

Possible Answers:

10

9

11

8

7

Correct answer:

9

Explanation:

First, let  = speed of the helicopter,  = speed of the wind, and  = distance between city A and city B. Next, find the ratio of  to . Traveling against the wind: . Traveling with the wind: . Finally, set the equations equal to one another: .

Simplify the equation: .

Example Question #4 : How To Do Word Problems Where Two Quantities Are Unknown

Michael has  red shirts and  blue shirts, such that the ratio is  red shirts for every  blue shirts. What is the minimum number of shirts he can have?

Possible Answers:

There is insufficient information to answer the question.

Correct answer:

Explanation:

It really doesn't matter what  and are. What matters is the ratio given to us,  red:  blue. Let's assume that he can only have whole shirts. That means that the minimum number of red shirts he can have is , and the minimum number of blue is , giving us a total of .

Example Question #5 : How To Do Word Problems Where Two Quantities Are Unknown

Two cars leave a city at the same time. One heads east at  and the other heads west at . How far apart are they after  hours?

Possible Answers:

Correct answer:

Explanation:

Remember, . If we look at the car going east, this would mean:

If we look at the car going west, then:

Therefore, we need to add the two distances to find the total distance between them.

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