GED Math : Complex Operations
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Example Questions
Example Question #12 : Proportions And Percentages
John’s weight decreased from 320 pounds to 280 pounds. By what percent (nearest tenth, if applicable) did his weight decrease?
In a percent of decrease problem, the whole is the amount at the beginning of the time period, which here is 320 pounds. The part is the difference between the final and initial amounts, which here is 
Example Question #18 : Proportions And Percentages
To get on the ballot for Student Council at Cesar Chavez Junior High School, a student must turn in a petition with the signatures of 8% of all of the students. Chavez Junior High School has students from two grades - 311 seventh-grade students and 302 eighth-grade students.
Serena has a petition with the names of 32 seventh-grade students and 16 eight-grade students. Does she have the signatures she needs to get on the ballot, and if not, why not?
Serena cannot get on the ballot yet, because she does not have enough signatures overall.
Serena cannot get on the ballot yet, because she does not have enough signatures from eight-grade students.
Serena has the signatures she needs to get on the ballot.
Serena cannot get on the ballot yet, because she has too many signatures from seventh-grade students.
Serena cannot get on the ballot yet, because she does not have enough signatures overall.
There is only one qualification to get on the ballot - having 8% of the total number of students; this is the only thing we need to test.
Serena has 
of the students, which is not enough to get on the ballot.
The correct response is that Serena cannot get on the ballot yet, because she does not have enough signatures overall.
Example Question #13 : Proportions And Percentages
A salesman for a car dealership earns 15% commission on all sales. What will be his commission for a week if he sells three cars that week - a $35,000 SUV on Tuesday, a $24,000 car on Thursday, and a $40,000 van on Friday?
The total sale price of the cars he sells will be
15% of $99,000 is
which is the salesman's commission.
Example Question #51 : Complex Operations
A salesperson for a car dealership earns 20% commission on all sales. She has sold one vehicle this week - a $52,000 van on Tuesday, and today is Saturday. She would like to earn a total of $20,000 in commissions by week's end. At the very least, how much in sales must she accomplish today to meet her goal?
She has already met her goal.
First, we find out what the salesperson's total sales must be in order to reach her commissions goal:
She has already made $52,000 in sales, so she must sell at least
Example Question #21 : Proportions And Percentages
To get on the ballot for the student body president at McKinley High School, a student must turn in a petition with the signatures of 8% of the students from each of the three classes - sophomore, junior, and senior. There are 429 sophomores, 355 juniors, and 322 seniors enrolled at McKinley.
Greg has a petition with the signatures of 35 sophomores, 30 juniors, and 24 seniors. Can he get on the ballot with the signatures he has, and if not, why not?
Greg has the signatures he needs to get on the ballot.
Greg cannot get on the ballot yet, because he needs more signatures from seniors.
Greg cannot get on the ballot yet, because he needs more signatures from juniors.
Greg cannot get on the ballot yet, because he needs more signatures from sophomores.
Greg cannot get on the ballot yet, because he needs more signatures from seniors.
In order to answer the question, we must find out the percent of each class that has signed Greg's petition, and compare it to 8%.
Sophomores: 35 out of 429, which is 
Juniors: 30 out of 355,which is 
Seniors: 24 out of 322, which is 
Greg has sufficient signatures from sophomores and juniors, but not seniors.
Example Question #22 : Proportions And Percentages
Above is the menu for a coffee shop. The shop charges 7% sales tax.
Clara orders two large iced coffees, one large cappucino, one large cafe latte, and four butter croissants. She hands the cashier a twenty-dollar bill and a ten-dollar bill. How much will Clara get back in change?
The amount Clara has paid is insufficient.
Add up the pretax prices of Clara's items to find the total pretax amaount:
The tax is 7% of this, or
Add the amounts to get the cost after tax:
Since Clara has paid $30, her change will be
Example Question #51 : Complex Operations
To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 6,988 students, how many signatures must a student get to be on that ballot?
3% of a number is equal to that number multplied by 0.03, so 3% of the student population of 6,988 is
Round this to the nearest whole number, which is 210 students.
Example Question #21 : Proportions And Percentages
A quantity of a 10% acid solution is mixed with twice as much of a 20% acid solution.
Give the concentration, in percent, of acid in the resulting solution.
Since the correct answer is independent of the actual amounts, for simplicity's sake, we will assume that 100 mL of the 10% solution was used. Then the amount of 20% solution used was twice this, or 200 mL. The total amount of solution is 300 mL.
100 mL of 10% acid solution contains 
200 mL of 20% acid solution contains 
This is a total of 50 mL of acid out of 300 mL of solution.Therefore, the concentration of acid in the final mixture is
Example Question #381 : Ged Math
Laura currently makes $9.50 an hour working 30 hours a week. She has been told by her boss that she is getting a raise in her wages to $11.25 a week, and that she will be working a 40-hour week. By what percent will her weekly earnings increase (nearest whole)?
Laura currently makes
After her raise and her increase in work hours, she will make
an increase of 
This is an increase of
Example Question #21 : Proportions And Percentages
To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 6,988 students, how many signatures must a student get to be on that ballot?
3% of a number is equal to that number multplied by 0.03, so 3% of the student population of 6,988 is
Round this to the nearest whole number, which is 210 students.
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