Some algebra problems on the GED Mathematical Reasoning test are straightforward: Solve a given equation for x. Once you know the basic rules for solving, these are pretty simple. Things get a little more complicated in algebra when it comes to word problems, however. Sometimes, you’ll be given a word problem that requires you to WRITE the equation first and THEN solve it. You’ll need to translate English into “mathematical language” in order to make sure you set up your equations correctly, including variables and operations. To help you practice, here are five challenging GED algebra word problems. The answer key at the end of the post has detailed explanations to help you see the relationship between words and math in these types of questions.
Challenging GED Algebra Word Problems
1. The sum of three consecutive positive integers is 111. You need to determine what the three integers are. Which equation shows how you could solve the problem?
2. Levi sells his old car for $5,000. He buys a new car that is $2,600 less than five times the selling price of his old car. How much did Levi spend on his new car?
3. Audrey earns money each week by tutoring and by babysitting. She charges $30 an hour for tutoring, and $15 an hour for babysitting. In one week, she makes $120 in total. She works 5 hours each week. How many hours does she tutor, and how many hours does she babysit?
A) She tutors for 1 hour and babysits for 4 hours.
B) She tutors for 4 hours and babysits for 1 hour.
C) She tutors for 2 hours and babysits for 3 hours.
D) She tutors for 3 hours and babysits for 2 hours.
4. Oliver needs 340 grams of flour to make one batch of his biscuit recipe. He buys a bag of flour that is 2.27 kilograms. If he makes three batches of biscuits, how many grams of flour will he have left?
A) 1,020 grams
B) 1,190 grams
C) 1,250 grams
D) 1,930 grams
5. Iris is selling jewelry at a craft fair. She sells twice as many rings as bracelets. She sells three more necklaces than bracelets. She sells necklaces for $15, bracelets for $5, and rings for $10. She makes $245 at the craft fair. How many necklaces, bracelets, and rings did Iris sell?
A) 8 necklaces, 5 bracelets, and 10 rings
B) 5 necklaces, 10 bracelets, and 8 rings
C) 10 necklaces, 8 bracelets, and 5 rings
D) 5 necklaces, 8 bracelets, and 10 rings
You need to find three numbers that will add up to 111. The term “consecutive positive integers” essentially means three whole numbers in a row, such as 1, 2, and 3. You can let the first number in the series be x. Since the numbers are consecutive, the second number in the series will be 1 more than x, and the third number in the series will be 2 more than x, so the three consecutive integers are x, x+1, and x+2. The sum of these three terms needs to be 111, so your equation will be:
You can simplify the expression by combining like terms—in this example, adding the variables and then adding the constants.
If you wanted to solve for x, you would isolate the variable by subtracting 3 from both sides, then dividing by 3:
So, the 3 consecutive integers are 36, 37, and 38.
This problem involves translating the words into mathematical expressions.
|five times||5x||The phrase "five times" tells you that you will multiply some amount by 5. Use x to represent the unknown value.|
|Levi sells his old car for $5,000.||5(5000)||Since you are looking for an amount that is five times the selling price of his old car, and you know that he sold his old car for 5,000, x, the amount you are multiplying by 5, is equal to 5,000.|
|$2,600 less||-2600||This phrase tells you that you will subtract 2600 from some amount.|
|$2,600 less than five times the selling price of his old car||5(5000)-2600||You know that you are looking for $2,600 less than five times the selling price of his old car, which is the term you found previously.|
|How much did Levi spend on his new car?||y||You are trying to find out how much Levi paid for his new car. This is your unknown variable.|
|He buys a new car that is $2,600 less than five times the selling price of his old car.||y=5(5,000)-2,600||This sentence tells you that the price of his new car equals the expression you found previously.|
Now, you just need to solve for y:
This problem involves a system of equations, since you have multiple unknown variables.
- Let x be the number of hours Audrey tutors each week.
- Let y be the number of hours she babysits each week.
The first equation is quite simple to set up, since you know that she works 5 hours each week:
Use the information about the money Audrey earns to set up the second equation.
You know she makes $30 an hour tutoring, and you already stated that the number of hours she tutors each week is x. So, the expression describing how much she makes each week tutoring is 30x.
You also know that she makes $15 an hour babysitting, and you already stated that the number of hours she babysits each week is y. So, the expression describing how much she makes each week babysitting is 15y.
Altogether, she makes $120 a week. So, your second equation tells you how to calculate the amount of money she earns weekly:
You can simplify this equation by dividing each term by 15:
So, you now have your two equations and can solve:
Isolate the x variable in the first equation:
Now, substitute this expression ofx into the second equation and solve for y:
So, she babysits for 2 hours each week. Now, you can use this information to solve for x using the first equation:
So, she tutors for 3 hours each week.
Your first step is to find out how many grams of flour Oliver uses. He uses 340 grams per batch of biscuits, and he makes three batches. So, you need to calculate:
He uses 1,020 grams. But, you cannot simply subtract this from the total mass of the bag of flour, because the bag of flour is stated in kilograms. Since the question asks for the amount of flour left in grams, you should convert the total mass of the bag of flour to grams. 1,000 grams are equal to 1 kilogram. To convert, multiply 2.27 by 1000.
2.27(1000)= 2270 grams
Now, subtract the amount of grams of flour Oliver used from the total grams in the bag of flour:
This seems like a system of equations because there are multiple unknown amounts, and you COULD solve it that way, but you would need three equations so it would get a little complicated. In this case, though, there’s an easier way. Since the number of rings and necklaces Iris sells is given in terms relative to the number of bracelets she sells, you really only have one unknown variable: the number of bracelets Iris sells.
Let the number of bracelets Iris sells be x. You know she sells each bracelet for $5. So, the amount of money she makes from bracelets is given by the expression 5x. Iris sells twice as many rings as bracelets. So, the number of rings she will sell is 2x. You know she sells each ring for $10. So, the amount of money she makes from rings is given by the expression 10(2x). Iris sells three more necklaces than bracelets. So, the number of necklaces she sells is x+3. You know she sells each necklace for $15. So, the amount of money she makes from necklaces is given by the expression
It might help to make a table to help you organize all of the information in this problem. Fill out the table as you parse each piece of information in the problem.
|number of bracelets sold||x|
|price of each bracelet||$5|
|money received for bracelets||5x|
|number of rings sold||2x|
|price of each ring||$10|
|money received for rings||10(2x) = 20x|
|number of necklaces sold||x+3|
|price of each necklace||$15|
|money received for necklaces||15(x+3)=15x+45|
You know that in total she made $245 at the craft fair. So, the sum of the money received for bracelets, rings, and necklaces, will equal 245:
So, you have one equation that you can solve for x, which is the number of bracelets sold:
Remember that x equals the number of bracelets sold. The problem asks you to find the number of bracelets, rings, and necklaces sold. Since the number of each type of jewelry sold is given in relative terms, once you know the number of bracelets sold, you can find the number of rings and necklaces sold.
The number of rings sold is 2x, so 2x=2(5)=10.
The number of necklaces sold is x+3, so x+3=5+3=8.