How to do word problems where two quantities are unknown - Math
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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.
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.
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: 
.
First, let
Simplify the equation:
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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?
Rosie, Eileen and Sasha order a pizza. It is divided into
If there are
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
Since the pizza began as
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A farmer has 
units of fence. If he uses this to build a square fence, what will be the area enclosed by the fence?
A farmer has
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.
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
Plug that into our original equation.
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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?
Michael has
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 
.
It really doesn't matter what
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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?
Two cars leave a city at the same time. One heads east at
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.
Remember,
If we look at the car going west, then:
Therefore, we need to add the two distances to find the total distance between them.
Compare your answer with the correct one above
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.
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.
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: .
First, let
Simplify the equation:
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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?
Rosie, Eileen and Sasha order a pizza. It is divided into
If there are
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
Since the pizza began as
Compare your answer with the correct one above
A farmer has units of fence. If he uses this to build a square fence, what will be the area enclosed by the fence?
A farmer has
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.
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
Plug that into our original equation.
Compare your answer with the correct one above
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?
Michael has
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 .
It really doesn't matter what
Compare your answer with the correct one above
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?
Two cars leave a city at the same time. One heads east at
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.
Remember,
If we look at the car going west, then:
Therefore, we need to add the two distances to find the total distance between them.
Compare your answer with the correct one above
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.
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.
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: .
First, let
Simplify the equation:
Compare your answer with the correct one above
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?
Rosie, Eileen and Sasha order a pizza. It is divided into
If there are
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
Since the pizza began as
Compare your answer with the correct one above
A farmer has units of fence. If he uses this to build a square fence, what will be the area enclosed by the fence?
A farmer has
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.
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
Plug that into our original equation.
Compare your answer with the correct one above
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?
Michael has
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 .
It really doesn't matter what
Compare your answer with the correct one above
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?
Two cars leave a city at the same time. One heads east at
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.
Remember,
If we look at the car going west, then:
Therefore, we need to add the two distances to find the total distance between them.
Compare your answer with the correct one above
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.
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.
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: .
First, let
Simplify the equation:
Compare your answer with the correct one above
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?
Rosie, Eileen and Sasha order a pizza. It is divided into
If there are
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
Since the pizza began as
Compare your answer with the correct one above
A farmer has units of fence. If he uses this to build a square fence, what will be the area enclosed by the fence?
A farmer has
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.
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
Plug that into our original equation.
Compare your answer with the correct one above
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?
Michael has
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 .
It really doesn't matter what
Compare your answer with the correct one above
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?
Two cars leave a city at the same time. One heads east at
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.
Remember,
If we look at the car going west, then:
Therefore, we need to add the two distances to find the total distance between them.
Compare your answer with the correct one above