HSPT Math : Problem Solving
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #3 : How To Solve Arithmetic Word Problems
There are 500 students at the high school. There are only two menu options: chicken or fish. If 15% of students ordered fish, how many students ordered chicken?
If 15% of students ordered fish, then 85% of the students must have ordered chicken. Then multiply 85% or 
Example Question #63 : Algebraic Concepts
A college has 
Let 
Then we can set up the following proportion:
Example Question #834 : Isee Upper Level (Grades 9 12) Mathematics Achievement
In appreciation for a job well done, Loretta is being awarded a bonus equal to 7.5% of the salary she earned over the last two years. Her monthly salary over the last twelve months was $3,500 per month; she received a raise of $500 per month twelve months ago. What is the amount of the bonus?
Loretta earned $3,000 per month for twelve months, and $3,500 per month for the following twelve months. This is a total of
earned over two years. 7.5% of this is
the amount of Loretta's bonus.
Example Question #91 : Problem Solving
A class has 25 students. If 60% of them are boys, how many students are girls?
8
9
15
20
10
10
We know that 40% of the class are girls because 60% are boys. To express 40% as a fraction of the 25 total students, we set up a proportion to find the number of girls in the class.
When solving for 
Example Question #31 : How To Work With Percentages
Fifteen percent of the students in the classroom brought their lunch from home. If 9 students brought their lunch from home, how many students are in the classroom total?
135
60
6
50
60
You can think of the total number of students in the classroom as an unknown variable, 
You can set up an equation that includes 
Total Amount x Percent = Part of Total Amount
You use 
Now you can algebraically solve for 
Therefore there are 60 total students.
Example Question #4 : How To Solve Arithmetic Word Problems
Candidate A gets 
Candidate B gets 35% of the votes.
If 2.8 million people votes, how many more votes than Candidate A did Candidate B receive?
First we need to get 
Now we multiply this fraction by 2.8 million, which reduces nicely to 
Example Question #92 : Problem Solving
In a poll, Camille learned that 
In order to solve this problem, you must first solve for what percentage of the entire group comprise of Spanish-speaking students. To do this, divide the total amount of Spanish-speaking students by the total number of students.
Multiply this number by 100 and round up in order to get your percentage.
Then, multiply this number times the total degrees in a circle to find out the measurement of the piece representing Spanish-speaking students on the pie chart.
Round up:
Example Question #93 : Problem Solving
What is 
The meaning of a percent is the number over 100 parts.
Example Question #34 : Percentages
If 
When dividing 
Example Question #42 : Percentage
A class with 
The percentage of students who attended the field trip can be found by dividing the number present by the total number of students. Here this is 
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