• When you are dealing with money, it is important to have strategies for calculating or estimating percents quickly and accurately. In this lesson, you will look at a variety of situations involving money in which percents are important. One of these is calculating the amount of the tip (or gratuity) for a meal at a restaurant and the other is calculating simple interest. When the amount added or paid is determined only by the original amount borrowed or deposited, this is called simple interest. As you work with your team today, these questions could help guide yourdiscussions:
  • Is there another strategy that will work?
  • Is there a more efficient way?
  • Is the answer reasonable?
  • 9-70. WHAT IS THE TIP?
  • Kendra has three friends who have birthdays during the summer. Every year she buys them dinner to celebrate. This year, the bill for dinner came to$125.
  • Kendra says,“I like to leave a tip for our waitperson for good service, but I never know how much money to leave.”
  • Rhonda replies,“I always leave a 15% tip.”
  • Then Shirley says, “But our service was really good, so I think you should leave 20%.”
  • Without using a calculator, find two different ways to calculate the 15% tip that Rhonda thinks they shouldleave.
  • Findtwo different ways to compute a 20% tip
    without using acalculator.
  • Rhondaand Shirley were not able to convince each other of how much of a tip to leave, so Daijah said, “Let’s compromise and leave an 18% tip.” Find two different ways to calculate the 18% tip that they will leave.
  • 9-71.Lorrayne’s father wanted to teach her about saving money. He offered to act as a bank and keep her money safe for her. He even said he would pay her 4% simple interest on her money for a year. In other words, if she gave him money to keep for her, after one year, he would add 4% of the original amount (the principal) to hersavings.
  • Lorrayne told Jill and Mickie about this. They quickly went to their parents to propose similar plans. Below is information about the arrangement each girl made with herparents.
  • Lorrayne says,“I gave my dad $1000, and he will pay 4% interest.”
  • Jill states,“My mom offered to pay me 5.5% interest, and I gave her my $800.”
  • Mickie explains, “I gave my $950 to my parents. They will pay 4.5% interest.”
  • After one year, how much interest will each girl have earned? Show yourwork.
  • Howmuch money will each girl have after one year?
  • 9-72. Johnwants to borrow $15 from Tyler. “C’mon!” says John. “I’ll make a deal with you. If you loan me the $15, I will pay it back to you with 35% interest next week. OrI’ll pay you back the $15 and an extra $5. Yourchoice.”
  • If Tyler agrees to loan John the money, which deal will give Tyler more money in the end: the 35% interest or the extra $5? Explain yourchoice.
  • 9-73. Ginaand Matt both arranged savings plans with their parents. Gina’s parents promised to pay 8.5% interest. Matt’s parents offered only 3% interest each year. When Gina heard about Matt’s arrangement, she said, “That means that I am going to have more money than you nextyear!”
  • Discuss Gina’s comment with your team and explain whether you agree or disagree andwhy.
  • 9-74. LEARNING LOG
  • In a Learning Log entry, describe strategies for calculating percents without a calculator. Be sure to include examples to demonstrate your thinking. Title this entry “Calculating Percents Mentally” and label it with today’sdate.

Calculating Percents by Composition

  • Calculating 10% ofa number and 1% of a number will help you calculate other percentsbycomposition.
  • To calculate 13% of 25, you can think of 10%of 25 + 3(1%of 25).
  • 10% of 25 ⇒of 25 = 2.5 and
  • 1% of 25 ⇒of 25 = 0.25 so
  • 13% of 25 ⇒ 2.5 + 3(0.25) ⇒ 2.5 + 0.75 = 3.25
  • To calculate 19% of 4500, you can think of 2(10%of 4500) − 1% of 4500.
  • 10% of 4500 ⇒of 4500 = 450 and
  • 1% of 4500 ⇒of 4500 = 45 so
  • 19% of 4500 ⇒ 2(450) − 45 ⇒ 900 − 45 = 855
  • 9-75. Find each of the following values or percents without using a calculator. Showyour work or explain your thinking for eachproblem. Homework Help ✎
  • 22% of what amount is $88
  • $35 is what % of $175
  • 94% of $130 is what amount?
  • 9-76. Calculate the sale price of each of the following discounteditems. Homework Help ✎
  • A car originally priced at $15,500 is discounted25%.
  • A pair of shoes originally priced at $39 is discounted15%.
  • 9-77. The shaded surface of the figure at right has an area of 18 squarecm. The volume of the rectangular prism is 131.4 cubic cm. Homework Help ✎
  • What is the height? Explain how youknow.
  • If the dimensions of the shaded rectangle have a ratio of 2:1, find the surface area of the figure. Show your work.
  • 9-78. Jenna was building a fence for her new sheep’s pen. She needs a total of 40linear feet of lumber. Some of her neighbors have agreed to give her lumber, and she wants to know if she hasenough. Homework Help ✎
  • Neighbor Jim will give her a board that he says is8feet long. Neighbor Malia will give her two boards that she says are each 126 inches long. What is the total combined length of lumber Jenna has received?
  • Neighbor Mike called and offered to donate a board that is 400 centimeters long. Jenna found the conversion information at right. Help her decide if she has enough lumber to make herpen.
  • 9-79. This problem is a checkpoint for solving one-step equations. It will be referred to as Checkpoint 9B.
  • Solve each equation. Homework Help ✎
  • x − 13 = 49
  • 4m = 68
  • 78 = y + 19
  • 5y = 17
  • Checkyour answers by referring to the Checkpoint 9B materials.
  • Ideally, at this point you are comfortable working with these types of problems and can solve them correctly. If you feel that youneed more confidence when solving these types of problems, then review theCheckpoint 9Bmaterials and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.