Mastering Percentage Word Problems

Table of Contents:

1. Introduction
2. Solving Percentage Word Problems
   1. Problem 1: Finding the Total Number of Students in Seventh Grade
      • Mental Math Approach
      • Proportion Approach
   2. Problem 2: Finding a Percentage of a Number
      • Algebraic Equation Approach
      • Proportion Approach
   3. Problem 3: Finding the Percentage of Students with Brown Hair
      • Percentage Calculation Approach
3. Conclusion

Solving Percentage Word Problems

Problem 1: Finding the Total Number of Students in Seventh Grade

In this problem, We Are given that 65 out of the seventh-grade students made the honor Roll, which represents 25% of the seventh-grade class. We need to determine the total number of students in seventh grade.

Mental Math Approach

We can use mental math to estimate the total number of students. Since 25% is equivalent to one-fourth, we can infer that 65 is one-fourth of the total number of students. Multiplying 65 by four, we find that the total number of students in seventh grade is 260.

Proportion Approach

Alternatively, we can use a proportion to solve this problem. Setting up the proportion with 65 as the part and the total as "x," we can cross multiply and solve for "x." By dividing 65 by four, we find that 25 can fit into 65 twice, resulting in 50. Subtracting 50 from 65 gives us 15. Then, since 25 goes into 150 six times exactly, we can place a zero, yielding a total of 600. Therefore, the total number of students in seventh grade is 260.

Problem 2: Finding a Percentage of a Number

In this problem, we are given that 30% of an unknown number "X" is equal to 225. We are required to find 76% of "X."

Algebraic Equation Approach

To solve this problem, we can set up an algebraic equation. We can rewrite 30% as 0.3 in decimal form and express it as 0.3X = 225. Dividing both sides of the equation by 0.3, we find that X is equal to 750.

Proportion Approach

We can also use proportions to solve this problem. By setting up a proportion with 30 as the part and 100 as the total, we can cross multiply and find the value of "X." Dividing 30 into 225 gives us 7.5. Thus, X is equal to 750.

Now that we know the value of "X," we can determine 76% of it.

Problem 3: Finding the Percentage of Students with Brown Hair

In this problem, we are informed that 88 out of 244 students at a middle school have brown hair. We need to calculate the percentage of students with brown hair, rounded to the nearest tenth of a percent.

To find the percentage, we can divide the numerator (88) by the denominator (244). Simplifying this as a decimal, we have 0.3606557377.

Since we need to round to the nearest tenth of a percent, we look at the hundredth place digit, which is 6. Since 6 is between 5 and 9, we round the tenth place digit up, resulting in a final percentage of approximately 36.1%.

Conclusion

Solving percentage word problems involves various approaches, such as mental math, proportion setting, and algebraic equations. By applying these methods, we can find the total number of students, calculate percentages, and provide accurate solutions to different types of percentage word problems. Consider practicing these techniques to enhance your problem-solving skills.