SSAT Upper Level Math : Algebra

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #23 : Algebraic Word Problems

John sells apples for  per bunch and watermelons for  a piece.  He made  today and sold  watermelons. How many bunches of apples did he sell?

Possible Answers:

Correct answer:

Explanation:

You must first set up a revenue equation where  represents the number of bunches of apples sold and  represents the number of watermelons sold.  

This would give us the equation 

.  

The problem gives us both  and  and when we plug those values in we get 

 

or

.

Now you must get  by itself.  

First, subtract  from both sides leaving .  

Then divide both sides by  to get your answer .

Example Question #24 : Algebraic Word Problems

A class of 60 students is divided into two groups; one group has eight less than the other; how many are in each group?

Possible Answers:

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

To solve this algebraic word problem, first set up an equation:

The variable  represents the amount of people in the group.

Add 

Isolate the variable by adding 8 to both sides of the equation:

Check to make sure that the two conditions of the problem have been met.

Condition one: The two numbers added together must equal 60.

Condition two. One of the numbers is eight less than the other.

Because these two conditions have been met, there are  people in one group and  people in the second group.

Example Question #25 : Algebraic Word Problems

The area of a rectangle is . The width is five less than the length. What is the length and width of the rectangle? 

Possible Answers:

 is the length;  is also the width

 is the length;  is the width

 is the length;  is the width

 is the length;  is the width

Correct answer:

 is the length;  is the width

Explanation:

The formula for computing the area of a rectangle is Area = l x w, where l = length and w = width.

In this algebraic word problem, let the variable  represent the length and  will represent the width of the rectangle.

Write an equation:

Distribute the variable  to what is inside the parentheses:

Set that expression equal to zero by subtracting 36 from both sides:

Factor using the FOIL Method:

Set each equal to zero to find the values of x that make this expression true:

There are two possible values for  and 

Because a dimension cannot be a negative integer, reject  Therefore . This is the measurement of the length of the rectangle.

 represents the width of the rectangle.

Now check to see if the two conditions are met.

Condition 1: Area = length x width

Condition 2: The width is 5cm less than the length.

Therefore  is the length and  is the width of this rectangle.

 

 

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