Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Setting Up Equations

If Bob's age is  years old and Jack is  more than  times Bob's age, then express Jack's age in terms of .

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. 

 more than means that you need to add  to something. 

 times something means that you need to multiply  to Bob's age which is 

Now we can combine them to have an expression of .

Example Question #12 : Setting Up Equations

There are  marbles in a jar. There are  types of color: red, blue, green and yellow. There are  red marbles,  blue marbles,  green marbles. Find an equation to represent the number of yellow marbles.

Possible Answers:

Correct answer:

Explanation:

We have  known values and  unknown value. We have a total and that these  colors add up to .

Let's represent the colors with variables corresponding to the first letter of the color. .

Now, plug in the values that are known. Final answer is 

To simplify we add the constants which results in:

Example Question #361 : Basic Single Variable Algebra

Express as an equation.

Difference between  times  and the quotient of  and  is  more than  times 

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. What a difference means, is that  is the first number subtracting .

The  part is  times something means that you need to multiply  to something which is .

The  part is quotient. 

Anytime you take a quotient of  and  is the in the numerator and  is in the denominator. Therefore the expression is 

Anytime you see "is" means equal.  

 more than means that you need to add  to something.

That something is  multipled by  or .

Let's just combine them to have an expression of 

Example Question #14 : Setting Up Equations

Jon needs to make four monthly deposits. The first month, he deposits  dollars. Each month after he adds  dollars to the previous month's deposit. Find an equation to solve for  if the total amount of money deposited for the four months is 

Possible Answers:

Correct answer:

Explanation:

Let's translate into math equations.

First month is  Then for the next month, he adds  to the previous month or  Then, for the next month, he adds another  to the previous month which was  By adding another , this month becomes  For the fourth month, it's just another   added to the previous month which was  The fourth month becomes .

With the total given, lets combine the expressions to get .

Simplifying this we get:

Example Question #11 : Setting Up Equations

Express as an equation.

The sum of  and  is 

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. The sum of something means adding. So that would be . Is means equals something. Putting it all together, we get 

Example Question #16 : Setting Up Equations

Express as an equation.

The difference between  and  is 

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. Difference means subtracting. So we are subtracting  and . Is means equal something. Putting it all together, we have .

Example Question #17 : Setting Up Equations

Express as an equation. The product of  and  is the sum of  and 

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. The product of something means multiplying. So we have . The sum of something means adding. So that would be . Is means equals something. Putting it together, we have 

Example Question #11 : Equations

Express as an equation. The quotient of  and  is the difference of  and  times sum of  and .

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. Quotient means dividing, so we have . When it's  and  will always be at the numerator of the fraction. Is means equal something. Difference is subtracting and we are subtracting  with  times sum of  and . Times means multiplying and sum means addition. We are multiplying  with . There must be parentheses as the sum of  and  is an expression. Putting it all together, we get 

Example Question #19 : Setting Up Equations

Express as an equation.

The square root of  is the sum of  and  squared.

Possible Answers:

Correct answer:

Explanation:

Take every word and translate into math. Square root means using a radical sign. So we have . Is means equal something. Next, sum is addition so we have . Since it's squared, we have the whole thing in parentheses raised to the second power like so: . It is tempting to think it's  but if it was, then it should say sum of  and  square. So final answer is 

Example Question #11 : Equations

Solve for  in the following equation:

Possible Answers:

Correct answer:

Explanation:

Starting with the equation , you want to collect like terms.

Put all of the numbers on one side, and leave only the variable on the other side.

The first step is to subtract  from both sides.

You get .

The next step is to divide both sides by  to get the final answer, .

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