Setting Up Equations - Algebra 2
Card 1 of 448
Write the following equation:
Shirts are 15 dollars and jeans are 30 dollars.
The total amount of money you made from selling shirts and jeans is at least 200 dollars.
Write the following equation:
Shirts are 15 dollars and jeans are 30 dollars.
The total amount of money you made from selling shirts and jeans is at least 200 dollars.
Tap to reveal answer
You know that shirts sell for 15 dollars and jeans sell for 30 dollars.
The tricky part is knowing that you sold at least 200 dollars worth of merchandise.
This means that you could have sold more than 200 dollars, but no less than that.
This means that your answer is
You know that shirts sell for 15 dollars and jeans sell for 30 dollars.
The tricky part is knowing that you sold at least 200 dollars worth of merchandise.
This means that you could have sold more than 200 dollars, but no less than that.
This means that your answer is
← Didn't Know|Knew It →
Write in slope-intercept form
Write in slope-intercept form
Tap to reveal answer
Recall the form for slope-intercept as follows.
where 
represents the slope and 
is the y-intercept.
Given the equation in this question, first distribute the one fourth to both terms inside the parentheses.
Next, subtract two from both sides to isolate y.
This results in the slope-intercept form of the equation.
Recall the form for slope-intercept as follows.
where
Given the equation in this question, first distribute the one fourth to both terms inside the parentheses.
Next, subtract two from both sides to isolate y.
This results in the slope-intercept form of the equation.
← Didn't Know|Knew It →
Corey buys potatoes for $2.25 per pound and quinoa for $5.75 per pound. If Corey buys p pounds of potatoes and q pounds of quinoa for $37.25, which of the equations below represents his transaction?
Corey buys potatoes for $2.25 per pound and quinoa for $5.75 per pound. If Corey buys p pounds of potatoes and q pounds of quinoa for $37.25, which of the equations below represents his transaction?
Tap to reveal answer
The cost for p pounds of potatoes is 2.25_p_ and the cost for q pounds of quinoa is 5.75_q_. The total amount Corey pays is the sum of the cost for potatoes and the cost for quinoa.
2.25_p_ + 5.75_q_ = 37.25
The cost for p pounds of potatoes is 2.25_p_ and the cost for q pounds of quinoa is 5.75_q_. The total amount Corey pays is the sum of the cost for potatoes and the cost for quinoa.
2.25_p_ + 5.75_q_ = 37.25
← Didn't Know|Knew It →
Beetle A runs in a straight line for 30cm before bumping into Beetle B, who then runs for another 90cm at a rate 3 times faster than Beetle A.
What is the rate of Beetle B?
Beetle A runs in a straight line for 30cm before bumping into Beetle B, who then runs for another 90cm at a rate 3 times faster than Beetle A.
What is the rate of Beetle B?
Tap to reveal answer
Knowing:
Beetle A:
Beetle B:
Combined:
Multiply each term by LCD (3x) to get:
Knowing:
Beetle A:
Beetle B:
Combined:
Multiply each term by LCD (3x) to get:
← Didn't Know|Knew It →
Set up the following equation: Three less than the square of a number is eleven.
Set up the following equation: Three less than the square of a number is eleven.
Tap to reveal answer
Split up the question into parts.
The square of a number: 
Three less than the square of a number: 
Is eleven: 
Combine the terms.
The answer is: 
Split up the question into parts.
The square of a number:
Three less than the square of a number:
Is eleven:
Combine the terms.
The answer is:
← Didn't Know|Knew It →
Set up the equation: The square root of six less than twice a number is equal to nine.
Set up the equation: The square root of six less than twice a number is equal to nine.
Tap to reveal answer
Split up the sentence into parts.
Twice a number: 
Six less than twice a number: 
The square root of six less than twice a number: 
Is equal to nine: 
The answer is: 
Split up the sentence into parts.
Twice a number:
Six less than twice a number:
The square root of six less than twice a number:
Is equal to nine:
The answer is:
← Didn't Know|Knew It →
Set up the equation: The sum of two times a number and forty is equal to sixteen.
Set up the equation: The sum of two times a number and forty is equal to sixteen.
Tap to reveal answer
Break up the problem into parts.
Two times a number: 
The sum of two times a number and forty: 
Is equal to sixteen: 
Combine the terms to form the equation.
The answer is: 
Break up the problem into parts.
Two times a number:
The sum of two times a number and forty:
Is equal to sixteen:
Combine the terms to form the equation.
The answer is:
← Didn't Know|Knew It →
Set up the following equation: The square root of a three times a number cubed is eight.
Set up the following equation: The square root of a three times a number cubed is eight.
Tap to reveal answer
Split up the sentence into parts.
A number cubed: 
Three times a number cubed: 
The square root of a three times a number cubed: 
Is eight: 
Combine the terms to form the equation.
The answer is: 
Split up the sentence into parts.
A number cubed:
Three times a number cubed:
The square root of a three times a number cubed:
Is eight:
Combine the terms to form the equation.
The answer is:
← Didn't Know|Knew It →
Set up the equation:
The difference of six and a number squared is four.
Set up the equation:
The difference of six and a number squared is four.
Tap to reveal answer
Write the following sentence by parts.
A number squared: 
The difference of six and a number squared: 
Is four: 
Combine the parts to write an equation.
The answer is: 
Write the following sentence by parts.
A number squared:
The difference of six and a number squared:
Is four:
Combine the parts to write an equation.
The answer is:
← Didn't Know|Knew It →
Set up the equation: Four more than seven times a number is fifty.
Set up the equation: Four more than seven times a number is fifty.
Tap to reveal answer
Break up the sentence into parts.
Seven times a number: 
Four more than seven times a number: 
Is fifty: 
Combine the terms to form the equation.
The answer is: 
Break up the sentence into parts.
Seven times a number:
Four more than seven times a number:
Is fifty:
Combine the terms to form the equation.
The answer is:
← Didn't Know|Knew It →
Set up the equation: Six less than four times a number squared is eight.
Set up the equation: Six less than four times a number squared is eight.
Tap to reveal answer
Split up the sentence into parts.
Four times a number squared: 
Six less than four times a number squared: 
Is eight: 
Combine the terms to form an equation.
The answer is: 
Split up the sentence into parts.
Four times a number squared:
Six less than four times a number squared:
Is eight:
Combine the terms to form an equation.
The answer is:
← Didn't Know|Knew It →
Set up the equation: Four less than a number is at least sixty.
Set up the equation: Four less than a number is at least sixty.
Tap to reveal answer
Break up the sentence into parts. Let the number be 
.
Four less than a number: 
Is at least sixty: 
Combine the parts to form the inequality.
The answer is: 
Break up the sentence into parts. Let the number be
Four less than a number:
Is at least sixty:
Combine the parts to form the inequality.
The answer is:
← Didn't Know|Knew It →
Tom is painting a fence 
feet long. He starts at the West end of the fence and paints at a rate of 
feet per hour. After 
hours, Huck joins Tom and begins painting from the East end of the fence at a rate of 
feet per hour. After 
hours of the two boys painting at the same time, Tom leaves Huck to finish the job by himself.
If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?
Tom is painting a fence
If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?
Tap to reveal answer
Tom paints for a total of 
hours (2 on his own, 2 with Huck's help). Since he paints at a rate of 
feet per hour, use the formula
(or 
)
to determine the total length of the fence Tom paints.
feet
Subtracting this from the total length of the fence 
feet gives the length of the fence Tom will NOT paint: 
feet. If Huck finishes the job, he will paint that 
feet of the fence. Using 
, we can determine how long this will take Huck to do:
hours.
If Huck works 
hours and Tom works 
hours, he works 
more hours than Tom.
Tom paints for a total of
to determine the total length of the fence Tom paints.
Subtracting this from the total length of the fence
If Huck works
← Didn't Know|Knew It →
The monthly cost to insure your cars varies directly with the number of cars you own. Right now, you are paying $420 per month to insure 3 cars, but you plan to get 2 more cars, so that you will own 5 cars. How much does it cost to insure 5 cars monthly?
The monthly cost to insure your cars varies directly with the number of cars you own. Right now, you are paying $420 per month to insure 3 cars, but you plan to get 2 more cars, so that you will own 5 cars. How much does it cost to insure 5 cars monthly?
Tap to reveal answer
The statement, 'The monthly costly to insure your cars varies directly with the number of cars you own' can be mathematically expressed as 
. M is the monthly cost, C is the number of cars owned, and k is the constant of variation.
Given that it costs $420 a month to insure 3 cars, we can find the k-value.
Divide both sides by 3.
Now, we have the mathematical relationship.
Finding how much it costs to insure 5 cars can be found by substituting 5 for C and solving for M.
The statement, 'The monthly costly to insure your cars varies directly with the number of cars you own' can be mathematically expressed as
Given that it costs $420 a month to insure 3 cars, we can find the k-value.
Divide both sides by 3.
Now, we have the mathematical relationship.
Finding how much it costs to insure 5 cars can be found by substituting 5 for C and solving for M.
← Didn't Know|Knew It →
If the roots of a function are 
, what does the function look like in 
format?
If the roots of a function are
Tap to reveal answer
This is a FOIL problem. First, we must set up the problem in a form we can use to create the function. To do this we take the opposite sign of each of the numbers and place them in this format: 
.
Now we can FOIL.
First: 
Outside: 
Inside: 
Last: 
Then add them together to get 
.
Combine like terms to find the answer, which is 
.
This is a FOIL problem. First, we must set up the problem in a form we can use to create the function. To do this we take the opposite sign of each of the numbers and place them in this format:
Now we can FOIL.
First:
Outside:
Inside:
Last:
Then add them together to get
Combine like terms to find the answer, which is
← Didn't Know|Knew It →
Two numbers have a ratio of 5:6 and half of their sum is 22. What are the numbers?
Two numbers have a ratio of 5:6 and half of their sum is 22. What are the numbers?
Tap to reveal answer
Set up the equation:
Solve the equation:
Find the two numbers:
The two numbers have a ratio of 5:6, therefore the ratio can also be represented as:
The two numbers are 20 and 24.
Set up the equation:
Solve the equation:
Find the two numbers:
The two numbers have a ratio of 5:6, therefore the ratio can also be represented as:
The two numbers are 20 and 24.
← Didn't Know|Knew It →
What is the equation of the line that has a slope of 3 and passes through the point (3,-6)?
What is the equation of the line that has a slope of 3 and passes through the point (3,-6)?
Tap to reveal answer
The equation for a line in slope-intercept form is:
where 
and 
are the known coordinates (3,-6).
Substituting gives
,
and simplifying gives the final answer:
The equation for a line in slope-intercept form is:
where
Substituting gives
and simplifying gives the final answer:
← Didn't Know|Knew It →
Set up an equation that properly displays the information given.
Suzanne has a pack of multi-colored jelly beans. She wants to sort them into equal amounts to give out to her four friends, but not until she eats eight of them. If the total pack contains 60 jelly beans, then how many is each friend going to get?
Set up an equation that properly displays the information given.
Suzanne has a pack of multi-colored jelly beans. She wants to sort them into equal amounts to give out to her four friends, but not until she eats eight of them. If the total pack contains 60 jelly beans, then how many is each friend going to get?
Tap to reveal answer
Let 
be the number of jelly beans that each friend will receive. She has four friends, so the total number of jelly beans her friends will receive is 
. Suzanne eats another eight, so the equation can be written as 
.
Let
← Didn't Know|Knew It →
A circular tower stands surrounded by a circular moat. A bridge provides a passage over the moat to the tower. The distance from the outer edge of the moat to the center of the tower is 
meters. The area of the floor of tower is 
. How long is the bridge over the moat?
A circular tower stands surrounded by a circular moat. A bridge provides a passage over the moat to the tower. The distance from the outer edge of the moat to the center of the tower is
Tap to reveal answer
The distance from the outer edge of the moat to the center of the castle is the radius (100 m) of the larger circle formed by the outer edge of the circular moat.
The radius of the tower's floor (found using the area of the floor), needs to be subracted from 100 m to find the distance fo the bridge.
The distance from the outer edge of the moat to the center of the castle is the radius (100 m) of the larger circle formed by the outer edge of the circular moat.
The radius of the tower's floor (found using the area of the floor), needs to be subracted from 100 m to find the distance fo the bridge.
← Didn't Know|Knew It →
Your friend goes on a diet to lose a little weight. He starts at 
pounds and cuts his calories by 
a day. Write a linear equation to express your friend's weight in pounds as a function of weeks on the diet. Hint: there are 
,
calories in a pound.
Your friend goes on a diet to lose a little weight. He starts at
Tap to reveal answer
The question asks for a relation between pounds lost and weeks on the diet. If each day your friend cuts 500 calories, the number of pounds he is losing per week is 1:
The rate of change, or slope, is therefore -1. The slope is negative because the independent variable (weight in pounds) is decreases as the dependent variable (time in weeks) increases. The y-intercept is 180, because that is how much your friend weighs at the start, when time = 0. Plugging these values into 
form, we end up with:
The question asks for a relation between pounds lost and weeks on the diet. If each day your friend cuts 500 calories, the number of pounds he is losing per week is 1:
The rate of change, or slope, is therefore -1. The slope is negative because the independent variable (weight in pounds) is decreases as the dependent variable (time in weeks) increases. The y-intercept is 180, because that is how much your friend weighs at the start, when time = 0. Plugging these values into
← Didn't Know|Knew It →