Your eyes open wide because the numbers are blurring across the math word problems. As the clock ticks louder, the sweat beads on your forehead. Unfortunately, you are unable to proceed because you cannot understand the context. Frustration builds. At the same time, you tap nervously. Time feels too fast and too slow. Here is how to solve math word problems to avoid the sinking fear of running out of time.
Three-Step Hack to Solving Math Word Problems Accurately
Read and analyze the problem
First, you must carefully read the problem to understand the situation and identify key details. Moreover, you can highlight important numbers, relationships, and constraints. Furthermore, break the problem into smaller parts. Ask what the question wants you to find. The analysis helps in percentage problems as well.
Formulate equations or relationships
Secondly, you must translate the problem into mathematical expressions using the identified details. In addition, you can assign variables to unknowns and create relationships that the problem provides. Also, ensure you account for all conditions. The step transforms the word problem into a solvable mathematical framework.
Solve and verify your answer
Lastly, solve the equations systematically using appropriate techniques. For example, you can use substitution or elimination. After obtaining the solution, plug it back into the problem to verify its accuracy. In other words, check if your answer makes sense according to the context.
Regular math word problems
Question 1
A certain Grocery store sells pens and pencils. In February, the store sold twice as many pens as pencils. In March, the store sold twice the number of pens that it sold in February and three times the number of pencils that it sold in February. If the total number of pens and pencils the store sold in February and March combined was 600, how many Pencils did the store sell in February?
Step 1: Define variables and relationships
Let the number of pencils sold in February be x. However, the shop sold twice as many pens were sold. Therefore, the term 2x will denote the pens sold in February.
Moreover, the pens sold in March were twice as more in February. In other words, 4x will symbolize the sales volume. Lastly, three times February’s pencils become 3x. Finally, the total is 600.
Step 2: Set up the equation
Combine sales for February and March:
So, the total sales the shop made in February and Match equals the revenue
In other words,
6x (pens from February in Match) + 4x (pencils sold in February and March) = 600
Next, simplify the equation:
10x=600
Step 3: Solve for x
Divide both sides by 10 to find x:
x=600/10=60
Thus, the number of pencils sold in February is 60.
Step 4: Verify the solution
In February, the store sold 60 pencils in addition to 120 pens.
Secondly, in March, the store sold 180 pencils and 240 pens.
Total: 60+120+180+240=600
Now, the solution checks out.
Question 2
Each month, Smith earns a commission of 9.5% of his total sales for the month, plus a salary of $4,500. If Smith earns $5,235 in a certain month, what were his total sales?
Step 1: Understand the earnings formula
In short, Smith’s total income equals his base salary plus commission. Therefore, let x become his sales. As a result, his income formula is:
4500+0.095S=5235
Now, we solve for S.
Step 2: Isolate S
First, subtract 4500 from both sides:
0.095S=5235−4500
0.095S=735
S=735
Step 3: Solve for S
Now, divide both sides by 0.095
S = 735/0.095 = 7,736.84
Therefore, Smith’s total sales are $7,736.84.
Step 4: Verify the calculation
Finally, we will calculate the commission:
0.095 × 7736.84 ≈ 735
Lastly, we will add the commission to the base salary.
4500+735=5235
Now, the solution checks out.
GRE Math Word Problems
Next, let’s explore some common math solutions frequently students encounter in the GRE, bank, and, also, admission exams. The invigilator designs math word problems to assess analytical skills and problem-solving abilities. Furthermore, such exams aim to evaluate a candidate’s aptitude for applying mathematical concepts to real-world scenarios. Therefore, success often depends on efficiently interpreting and solving problems using logic. Have a look below!
Question 1
There are 50 boys and girls signed up for a debate competition. There are 34 more boys than girls. How many boys have signed up to compete?
Step 1: Define variables
Foremost, let x denote the number of girls.
The math word problem mentions there are 34 more boys than girls. Therefore, the number of boys is x+34. Also, the total participants are 50.
Step 2: Set up the equation
Now, we combine boys and girls:
X + (x+34) =50
Next, we simplify for x
2x + 34 =50
Step 3: Solve for x
Subsequently, we will subtract 34 from both sides:
2x=16
Divide both sides of the equation by 2:
x=8
Thus, eight girls signed up for the debate competition. Therefore, 8+34=42 boys signed up to enter the debate.
Step 4: Verify the solution
Foremost, total participants are 8 + 42 = 50.
Subsequently, the difference is 42 – 8 = 34.
Therefore, the solution checks out.
Question 2
How many unique distributions are possible for three identical green balls and three identical red balls among six children, ensuring each child receives exactly one ball?
Step 1: Understand the problem
Foremost, there are six identical balls. In other words, the question mentions three green in addition to 3 red balls that someone is distributing among six children. However, each child must get exactly one ball. Therefore, we must use combinations.
Step 2: Calculate choices for green balls
Firstly, we choose three children to receive green balls:
6! / 3! = = 20
Step 3: Assign red balls
Thirdly, the remaining three children automatically receive red balls. In other words, the distributor has no further choices.
Step 4: Conclude the result
Therefore, the total number of unique distributions is 20. Moreover, every choice for green balls directly determines red ball recipients.
Common Mistakes in Solving Math Word Problems
Misunderstanding the problem
Frequently, 14.77% of students rush to solve math word problems without fully understanding them. They misinterpret key details or overlook important information. Therefore, carefully read the question in addition to identifying variables.
Ignoring units and context
Secondly, many students neglect to consider units. Math word problems include time, distance, or currency. As a result, it leads to incorrect answers. Also, always pay attention to the problem’s context and ensure calculations align with the units.
Skipping verification
After solving, students often fail to verify their answers. It can result in undetected errors or unrealistic results. Moreover, always recheck calculations, review assumptions, and confirm the solution. Verification ensures confidence in your answer. At the same time, it strengthens problem-solving skills.
Solve math word problems successfully!
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