An expression is defined as a mathematical symbol or group of symbols that represent a value. Throughout this study guide, we have seen many different kinds of variables, operations, and numbers.
Each of the following examples are expressions:
x
6y
6x + 3
Some questions on the ATI TEAS will test your understanding of translating word problems into expressions and equations. You use variables to represent unknown quantities.
For example:
Twice a number: 2x
Half the girls: 1/2g
Three less than the total number: t – 3
UNDERSTANDING WRITTEN EQUATIONS
An equation is defined as multiple expressions combined with an equal sign.
For example:
x = 100
x + 2= 20
4x(2 – 4) = 20
Some written equations will require the applicant to translate word problems in equations to solve. Like in written expressions, we use variables to represent unknown quantities.
Here are some examples of sentences and written equations:
There are 6 times as many boys as girls: b = 6g
Taylor paid $120 for 4 shirts and 2 pairs of pants: 4s + 2p = 120
UNDERSTANDING WRITTEN INEQUALITIES
An inequalities is defined as multiple expression combined with an inequality symbol such as <, >, £, and ³.
For example:
x ³ 100
x + 20 > 40
4x (2 – y) < 60
Some written equations will require the applicant to translate word problems into inequality equations to solve. Use variables to represent unknown quantities.
Here are some examples of sentences and written inequalities:
There are 6 times as many boys as girls: b > 6g
Taylor paid less than $120 for 4 shirts and 2 pairs of pants: 4s + 2p < 120
UNDERSTANDING ALGEBRA WORD PROBLEMS
In order to correctly solve algebra word problems, you must put all of these learned skills together. Be sure to take your time and write your equations or inequalities correctly.
For example: Jennifer and Calvin collect figurines. Together they have a total of 46 figurines. If Jennifer has 12 more figurines than Calvin, how many figurines does Calvin have in his collection?
Let j = the number of figurines Jennifer has and c = the number of figurines Calvin has. Now you can write the equation as:
c + j = 46 and c = j + 12.
Next, you can substitute the c in the first equation with c = j + 12.
j + 12 + j = 46
Now you can start to simplify.
j + 12 + j = 46 = 2j + 12 = 46
Subtract 12 from each side.
2j + 12 – 12 = 46 – 12
2j = 34
Divide 2 from both sides.
j = 17
Finish the equation and solve for c.
c = j + 12 then c = 17 +12 = 29
The final answer the equation is Jennifer has 29 figurines.
ATI TEAS Math Word Problems
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Question 1 of 8
1. Question
A hummer cost x dollars and a box of nails costs y dollars. Before tax, which of the following represents the cost to purchase the hummer and two boxes of nails?
Correct
The cost of a hummer is x. The cost of two boxes of nails would be 2y. The total cost would be x + 2y.
Incorrect
The cost of a hummer is x. The cost of two boxes of nails would be 2y. The total cost would be x + 2y.
Question 2 of 8
2. Question
Gabe and Kevin both collect model train cars. Together they have a total of 46 cars. If Gabe has 12 more cats than Kevin, how many cars does Gabe have in his collection?
Correct
Let k = the number of cars Kevin has and g = the number of cars Gabe has. Now you can write the equations g + k = 46 and g = k + 12. You can substitute the second equation into the first to get k + 12 + k = 46. Simplify that to 2k + 12 = 46. Subtract 12 from both sides to get 2k = 34. Divide both sides by 2 to get k = 17. Since the question asks for the number of train cars Gabe has, you need to solve for g. g = k + 12, so g = 17 + 12 = 29.
Incorrect
Let k = the number of cars Kevin has and g = the number of cars Gabe has. Now you can write the equations g + k = 46 and g = k + 12. You can substitute the second equation into the first to get k + 12 + k = 46. Simplify that to 2k + 12 = 46. Subtract 12 from both sides to get 2k = 34. Divide both sides by 2 to get k = 17. Since the question asks for the number of train cars Gabe has, you need to solve for g. g = k + 12, so g = 17 + 12 = 29.
Question 3 of 8
3. Question
Alexia has a total of 58 science textbooks. She has only biology and chemistry books, and she has 14 more chemistry books than biology books. How many biology books does Alexia have?
Correct
Let b = the number of biology books and c = the number of chemistry books. The total then is b + c = 58. You also know that alexia has 13 more chemistry books than biology books, so c = 14 + b. Substitute the second equation into the first to get b + 14 + b = 58. Simplify that to 14 + 2b = 58. Subtract 14 from both sides to get 2b = 44. Divide both sides by 2 to get b = 22.
Incorrect
Let b = the number of biology books and c = the number of chemistry books. The total then is b + c = 58. You also know that alexia has 13 more chemistry books than biology books, so c = 14 + b. Substitute the second equation into the first to get b + 14 + b = 58. Simplify that to 14 + 2b = 58. Subtract 14 from both sides to get 2b = 44. Divide both sides by 2 to get b = 22.
Question 4 of 8
4. Question
In a toy box, there are x dolls, y trucks, and z blocks. Which of the following expressions shows the percentage of blocks on the shelf?
Correct
First, formulate a question you can translate into an equation: what percent of the total number of toys is the number of blocks? Let A equal the percent you are looking for. Now the question translates to A / 100 x (x + y + z) = z . Multiply both sides by 100 to get A(x + y + z) = 100z.
Divide both sides by (x + y + z) to get A = 100z / ( x+y+z ) .
Incorrect
First, formulate a question you can translate into an equation: what percent of the total number of toys is the number of blocks? Let A equal the percent you are looking for. Now the question translates to A / 100 x (x + y + z) = z . Multiply both sides by 100 to get A(x + y + z) = 100z.
Divide both sides by (x + y + z) to get A = 100z / ( x+y+z ) .
Question 5 of 8
5. Question
The student-to-teacher ratio at a private school is 12:1. If there are 364 students enrolled for the next semester, which of the following shows how to find the number of teachers that will be needed to maintain the ratio?
Correct
Let t = the number of teachers needed. Set up proportion. The needed ratio is 12:1, so 364/t ≤ 12/1 . You need to use the less than or equal to symbol to be sure that there are no more than 12 students per teacher.
Incorrect
Let t = the number of teachers needed. Set up proportion. The needed ratio is 12:1, so 364/t ≤ 12/1 . You need to use the less than or equal to symbol to be sure that there are no more than 12 students per teacher.
Question 6 of 8
6. Question
If 5q + r = 27, and r = 2, then what is the value of q?
Correct
Plug in 2 for r to get 5q + 2 = 27. Now subtract 2 from both sides to get 5q = 25. Divide both sides by 5 to get q = 5.
Incorrect
Plug in 2 for r to get 5q + 2 = 27. Now subtract 2 from both sides to get 5q = 25. Divide both sides by 5 to get q = 5.
Question 7 of 8
7. Question
At a dental office, hygienists earn $14 per hour and lab technicians earn $12 per hour. If there are x hygienists and y lab technicians, which of the following represents their total hourly pay, in dollars?
Correct
The salary of the hygienists would be 14x. The salary of the lab technicians would be 12y. The total salary would be 14x + 12y.
Incorrect
The salary of the hygienists would be 14x. The salary of the lab technicians would be 12y. The total salary would be 14x + 12y.
Question 8 of 8
8. Question
Kendra is saving up to buy a snowboard. She has $90 so far. If she saves $30 per week, which of the following shows how many more weeks until she has at least $300?
Correct
Let x = the number of weeks. Kendra saves $30 per week, so that is 30x. Since she already has $90, now it is 30x + 90. She wants to have at least 300, so 30x + 90 > 300.
Incorrect
Let x = the number of weeks. Kendra saves $30 per week, so that is 30x. Since she already has $90, now it is 30x + 90. She wants to have at least 300, so 30x + 90 > 300.
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