Algebra II : Setting Up Equations
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Example Questions
Example Question #406 : Basic Single Variable Algebra
Billy donates two goats for every ten goats he buys from the farm. What is the equation that best represents this scenario? Let 
If Billy buys 10 goats, he will have donated 2 goats.
If Billy buys 20 goats, he will have donated 4 goats.
We can set up the equation by finding the slope of the two points 
Write the slope-intercept equation.
Substitute the known slope and a given point.
Write the equation.
Rewrite the equation in terms of 
The correct answer is:
Example Question #61 : Setting Up Equations
Set up the equation: The product of negative two and five less than twice a number is six.
Split up the sentence into parts.
Twice a number:
Five less than twice a number:
The product of negative two and five less than twice a number:
Is six:
Combine the terms.
The answer is:
Example Question #63 : Setting Up Equations
The first two scores on a student's exams in an algebra class were 
Let 
Multiplying both sides of the inequality by 
Adding like terms of the left-hand side of the inequality yields
Subtracting 
Hence, the student needs to achieve a score of at least 
Example Question #411 : Basic Single Variable Algebra
Set up the following equation: The difference of twice a number and the cube root of twice the number is ten.
Break up the sentence into parts.
Twice a number:
The cube root of twice the number:
The difference of twice a number and the cube root of twice the number:
Is ten:
Combine the parts to form the equation.
The answer is:
Example Question #412 : Basic Single Variable Algebra
Set up the equation: Three times the square root of twice a number is forty.
Break up the sentence into parts. Work the terms of the square root first.
Twice a number:
The square root of twice a number:
Three times the square root of twice a number:
Is forty:
Combine the terms to set up the equation.
The answer is:
Example Question #413 : Basic Single Variable Algebra
Set up the equation: Five less than eight times a number is fourteen.
Break up the sentence into parts.
Eight times a number:
Five less than eight times a number:
Is fourteen:
The answer is:
Example Question #414 : Basic Single Variable Algebra
Suppose Billy makes 
Determine how much Billy will earn per day. Since he works eight hours a day, multiply the hourly wage with the hours.
He will make 24 dollars a day.
For five days:
Billy will make 120 dollars per week.
Set up the equation.
The answer is:
Example Question #415 : Basic Single Variable Algebra
Set up the equation: Six times the quantity of three less than twice a number is eleven.
Break up the sentence into parts. Start by the inner quantity.
Three less than twice a number:
Six times the quantity of three less than twice a number:
Is eleven:
Combine the parts to form the equation.
The answer is:
Example Question #416 : Basic Single Variable Algebra
Set up the equation: Four less than seven times a number is eighty.
Break up the sentence into parts.
Seven times a number:
Four less than seven times a number:
Is eighty:
Combine the parts.
The answer is:
Example Question #411 : Basic Single Variable Algebra
Set up the equation: Eight less than twenty times a number is nine.
Split the sentence into parts.
Twenty times a number:
Eight less than twenty times a number:
Is nine:
Combine the terms.
The equation is:
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