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

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Example Questions

Example Question #122 : High School Math

A farmer has 100 units of fence. If he uses this to build a square fence, what will be the area enclosed by the fence?

Possible Answers:

100

625

10000

400

Correct answer:

625

Explanation:

Since we are looking at a square, the formula for the area of a square is A=s^2 .

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 P=4s when working with a square, for this problem 100=4s .

$\frac{100}{4}=s$

25=s

Plug that into our original equation.

A=s^2

A=25^2

A=625

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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

slice

Correct answer:

slices

Explanation:

Since the pizza began as slices and there are now slices remaining, a total of slices were eaten (because 10-3=7 ). 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.

s + 2s = 6

$\rightarrow 3s = 6$

$\rightarrow s = 2$ slices

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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:

Correct answer:

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: z=5 (x-y) . Traveling with the wind: z=4 (x+y) . Finally, set the equations equal to one another: 5x-5y=4x+4y .

Simplify the equation: x/y .

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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 .

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

Two cars leave a city at the same time. One heads east at $35\: mph$ and the other heads west at $67\: mph$ . How far apart are they after hours?

Possible Answers:

$96\text{ miles}$

$201\text{ miles}$

$105\text{ miles}$

$1.9\text{ miles}$

$306\text{ miles}$

Correct answer:

$306\text{ miles}$

Explanation:

Remember, $\text{distance}={\text{rate}}*{\text{time}}$ . If we look at the car going east, this would mean:

$\text{distance}={\text{rate}}*{\text{time}}$

$\text{distance}=35\: mph*3\text{ hours}$

$\text{distance}=105\text{ miles}$

If we look at the car going west, then:

$\text{distance}={\text{rate}}*{\text{time}}$

$\text{distance}=67\: mph*3\text{ hours}$

$\text{distance}=201\text{ miles}$

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

$T=201\text{ miles}+105 \text{ miles}$

$T=306\text{ miles}$

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

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #122 : High School Math

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

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

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

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

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