All SSAT Upper Level Math Resources
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?
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?
and
and
and
and
and
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?
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
is the length; is the width
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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