Comparing Quantities with Percent

Examples, videos, and solutions to help Grade 7 students understand that the whole is 100% and think of one quantity as a percent of another using the formula Quantity = Percent x Whole to problem-solve when given two terms out of three from a quantity, whole, and percent.

New York State Common Core Math Grade 7, Module 4, Lesson 3

Worksheets for Grade 7

Lesson 3 Student Outcomes

• Students use the context of a word problem to determine which of two quantities represents the whole.
• Students understand that the whole is 100% and think of one quantity as a percent of another using the formula Quantity = Percent x Whole to problem-solve when given two terms out of three from a quantity, whole, and percent.
• When comparing two quantities, students compute percent more or percent less using algebraic, numeric, and visual models.

Lesson 3 Summary

• Visual models or arithmetic methods can be used to solve problems that compare quantities with percents. • Equations can be used to solve percent problems using the basic equation: Quantity = Percent x Whole • “Quantity” in the new percent formula is the equivalent of “part” in the original percent formula.

Lesson 3 Classwork

Opening Exercise
If each 10 x 10 unit square represents one whole, then what percent is represented by the shaded region?
In the model above, 25% represents a quantity of students. How many students does the shaded region represent?

Exercises
1. There are 750 students in the 7th grade class and 625 students in the 8th grade class at Kent Middle School.
a. What percent is the 7th grade class of the 8th grade class at Kent Middle School?
b. The principal will have to increase the number of 8th grade teachers next year if the 7th grade enrollment exceeds 110% of the current 8th grade enrollment. Will she need to increase the number of teachers?
Explain your reasoning.
2. At Kent Middle School, there are 104 students in the band and 80 students in the choir. What percent of the number of students in the choir is the number of students in the band?
3. At Kent Middle School, breakfast costs $1.25 and lunch costs $3.75. What percent of the cost of lunch is the cost of breakfast?
4. Describe a real world situation that could be modeled using the equation: 398.4 = 0.83(x). Describe how the elements of the equation correspond with the real world quantities in your problem. Then solve your problem.

Lesson 3 Classwork

Example 1
a. The members of a club are making friendship bracelets to sell to raise money. Anna and Emily made 54 bracelets over the weekend. They need to produce 300 bracelets by the end of the week. What percent of the bracelets were they able to produce over the weekend?
b. Anna produced 32 bracelets of the 54 bracelets produced by Emily and Anna over the weekend. Compare the number of bracelets that Emily produced as a percent of those that Anna produced.
c. Compare the number of bracelets that Anna produced as a percent of those that Emily produced.

Example 2
The 42 students that play wind instruments represent 75% of the students who are in band. How many students are in band?

Example 3
Bob’s Tire Outlet sold a record number of tires last month. One salesman sold 165 tires. which was 60% of the tires sold in the month. What was the record number of tires sold?

Example 4
At Kent Middle School, there are 104 students in the band and 80 students in the choir. What percent of the number of students in the choir is the number of students in the band?

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