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Interest, Tax, Commissions, Percent Problems




 

Video solutions to help Grade 7 students learn how to solve real-world percent problems involving tax, gratuities, commissions, and fees.


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Common Core For Grade 7

New York State Common Core Math Grade 7, Module 4, Lesson 11


Lesson 11 Student Outcomes


• Students solve real-world percent problems involving tax, gratuities, commissions, and fees.
• Students solve word problems involving percent using equations, tables, and graphs.
• Students identify the constant of proportionality (tax rate, commission rate, etc.) in graphs, equations, tables, and in the context of the situation.

Lesson 11 Classwork

Opening Exercise

How are each of the following percent applications different, and how are they the same? First, describe how percents are used to solve each of the following problems. Then, solve each problem. Finally, compare your solution process for each.

a. Silvio earns 10% for each car sale he makes while working at a used car dealership. If he sells a used car for $2000, what is his commission?

b. Tu’s family stayed at a hotel for nights on their vacation. The hotel charged a 10% room tax, per night. How much did they pay in room taxes if the room cost per night?

c. Eric bought a new computer and printer online. He had to pay 10% in shipping fees. The items totaled $2000. How much did the shipping cost?

d. Selena had her wedding rehearsal dinner at a restaurant. The restaurant’s policy is that gratuity is included in the bill for large parties. Her father said the food and service were exceptional, so he wanted to leave an 10% extra tip on the total amount of the bill. If the dinner bill totaled $2000, how much money did her father leave as the extra tip?

Exercises 1–4
Show all work; a calculator may be used for calculations.
The school board has approved the addition of a new sports team at your school.
1. The district ordered 30 team uniforms and received a bill for $2,992.50. The total included a 5% discount.
a. The school needs to place another order for two more uniforms. The company said the discount will not apply because the discount only applies to orders of $1,000 or more. How much will the two uniforms cost?
b. The school district does not have to pay the 8% sales tax on the $2,992.50 purchase. Estimate the amount of sales tax the district saved on the $2,992.50 purchase. Explain how you arrived at your estimate.
c. A student who loses a uniform must pay a fee equal to 75% of the school’s cost of the uniform. For a uniform that cost the school $105, will the student owe more or less than 75% for the lost uniform? Explain how to use mental math to determine the answer.
d. Write an equation to represent the proportional relationship between the school’s cost of a uniform and the amount a student must pay for a lost uniform. Use u to represent the uniform cost and s to represent the amount a student must pay for a lost uniform. What is the constant of proportionality?

2. A taxpayer claims the new sports team caused his school taxes to increase by 2%.
a. Write an equation to show the relationship between the school taxes before and after a 2% increase. Use b to represent the dollar amount of school tax before the 2% increase and to represent the dollar amount of school tax after the 2% increase.
b. Use your equation to complete the table below, listing at least 5 pairs of values.
c. On graph paper, graph the relationship modeled by the equation in part (a). Be sure to label the axes and scale.
d. Is the relationship proportional? Explain how you know.
e. What is the constant of proportionality? What does it mean in the context of the situation?
f. If a tax payer’s school taxes rose from $4,000 to $4,020, was there a 2% increase? Justify your answer using your graph, table, or equation.

3. The sports booster club sold candles as a fundraiser to support the new team. They earn a commission on their candle sales (which means they receive a certain percentage of the total dollar amount sold). If the club gets to keep 30% of the money from the candle sales, what would the club's total sales have to be in order to make at least $500?

4. Christian's mom works at the concession stand during sporting events. She told him they buy candy bars for $0.75 each and mark them up 40% to sell at the concession stand. What is the amount of the mark up? How much does the concession stand charge for each candy bar?




Exercise 5
With your group, brainstorm solutions to the problems below. Prepare a poster that shows your solutions and math work. A calculator may be used for calculations.
5. For the next school year, the new soccer team will need to come up with $600.
a. Suppose the team earns $500 from the fundraiser at the start of the current school year, and the money is placed for one calendar year in a savings account earning 0.5% simple interest annually. How much money will the team still need to raise to meet next year’s expenses?
b. Jeff is a member of the new sports team. His dad owns a bakery. To help raise money for the team, Jeff's dad agrees to provide the team with cookies to sell at the concession stand for next year’s opening game. The team must pay back the bakery $0.25 for each cookie it sells. The concession stand usually sells about 60 to 80 baked goods per game. Using your answer from part (a), determine a percent markup for the cookies the team plans to sell at next year's opening game. Justify your answer.
c. Suppose the team ends up selling cookies at next year’s opening game. Find the percent error in the number of cookies that you estimated would be sold in your solution to part (b).
Percent Error |a - x|/|x| • 100%, where x is the exact value and a is the approximate value.


 
Lesson 10 Classwork

Interest = Principal x Rate x Time
I = P x r x t
I = Prt
• r is the percent of the principal that is paid over a period of time (usually per year).
• t is the time.
• r and t must be compatible. For example, if r is an annual interest rate, then t must be written in years.

Example 1: Can Money Grow? A Look at Simple Interest
Larry invests in a $100 savings plan. The plan pays 4 1/2% interest each year on his account balance.
a. How much money will Larry earn in interest after 3 years? After 5 years?
b. How can you find the balance of Larry’s account at the end of years?

Example 2: Time Other Than One Year
A savings bond earns simple interest at the rate 3% of each year. The interest is paid at the end of every month. How much interest will the bond have earned after three months?

Example 3: Solving for P, r, or t.
Mrs. Williams wants to know how long it will take an investment of $450 to earn $200 in interest if the yearly interest rate is 6.5% paid at the end of each year.

Lesson 11 Classwork

Opening Exercise






Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.



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