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# Solving Percent Problems: Jeans

# Solving Percent Problems: Lena

# Solving Percent Problems: Mrs. Abir

# Solving Percent Problems: Pablo

# Solving Percent Problems: TV

# Gallery Problems Exercise

## Overview

Allow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.

# Gallery Description

**Solving Percent Problems**

Students understand the structure of percent problems by analyzing many problems.

**Running a Clothing Store**

Students help the owner of a clothing store determine how to get the greatest profit.

**Less Fat**

Students determine the percentage of fat in whole milk.

**10% More**

Students evaluate three statements from Huey, Dewey, and Louie and determine which statement is correct.

**Free Space**

Students determine which of two hard drives has the most free space.

# Solving Percent Problems

# Answers

Lena

Jeans

Pablo

TV

Crime

Mrs. Abir

## Work Time

# Solving Percent Problems

For each problem, transfer the known information in the problem to the table to organize your thinking.

Solve the problem by yourself using a calculator and fill in the table.

In the “Operation” column, write the operation and value needed to change from the starting amount to the final amount, for example, “× 1.05” for a 5% increase.

Lena is raising rabbits. A month ago, she had 40 rabbits. Since then, the number of rabbits has increased by 45%. How many does she have now?

The label on a pair of denim jeans says that the jeans might shrink up to 5% in the wash. The inseam measures 80 centimeters. What is the least length to which the inseam can shrink?

Pablo now weighs 192 pounds. Over the past year, his weight has increased by 20%. What did Pablo weigh a year ago?

The price of a TV has dropped by 20% over the past five years. If the TV now costs $500, what did it cost five years ago?

Five years ago there were 360 crimes in a certain city. This last year there have been 864 crimes. What is the percent increase over this period?

Mrs. Abir bought a car for $8,000 last year. This year the car is worth $6,800. By what percentage did that car decrease in value?

HANDOUT: Solving Percent Problems: Lena

HANDOUT: Solving Percent Problems: Jeans

HANDOUT: Solving Percent Problems: Pablo

HANDOUT: Solving Percent Problems: TV

HANDOUT: Solving Percent Problems: Crime

HANDOUT: Solving Percent Problems: Mrs. Abir

# Running a Clothing Store

# Answers

- Apply the smallest discount to the item that brings in the most money before the discount, and so on.
- Assuming that the owner will be able to sell all the clothes, the greatest profit he can make is: $7230.00 – $3,150.00 = $4,080
- Answers will vary.

**Work Time**

# Running a Clothing Store

You are the manager of a local clothing store. The owner of the store has been able to buy a number of high-quality items at good prices. He wants to sell the clothes in the store at discounted prices with the goal of making the greatest possible profit.

The owner bought:

- 40 pairs of jeans for $40 a pair
- 50 T-shirts at $10 each
- 30 sweatshirts at $25 each
- 150 baseball caps at $2 each

The items are labeled with the suggested retail prices, seen in the chart here.

The owner provides you with four discount labels:

20% off, 25% off, 40% off, and 50% off.

- Assuming that the owner will be able to sell all the clothes, determine which discount label to use for each item for the store to make the greatest profit.
- Assuming that the owner will be able to sell all the clothes, what is the greatest profit he can make?
- Describe a situation that involves a percent increase of more than 100%.

# Less Fat

# Answers

The milk in the carton has 38% less fat than whole milk. The label “2% fat” means that for every 100 grams of low fat milk, there are 2 grams of fat. To solve this problem, figure out how many grams,

*x*, of fat are in 100 grams of whole milk. Then divide that number of grams by 100 grams to get the percentage of whole milk that is fat. Number of grams of fat per 100 grams of low fat milk2 =

*x*– 0.38*x*2 =

*x*(1 – 0.38)2 = 0.62

*x*

Solve for *x*:

*x* = 2 ÷ 0.62 ≈ 3.23 grams

The percentage of whole milk that is fat ≈ $\frac{3.23\text{grams}}{100\text{grams}}$ ≈ 3.23%.

**Work Time**

# Less Fat

A label of a carton of milk is shown here.

- What percent of whole milk is fat? Show your work.

# 10% More

# Answers

Huey: 100% + 10% = 110%

These percentages are taken with respect to the 45 oz box.

45 oz + 4.5 oz = 49.5 oz

Since 49.5 oz < 50 oz, there is more than 10% more in the 50 oz box. Huey is correct.

Dewey: Dewey equates 5 oz with 5%. The quantity 5 oz and the portion 5% would correspond only if the regular-size box held exactly 100 oz (since 105 oz is both 5 oz and 5% more than 100 oz).

Louie: Louie is taking the percentage of the 50 oz box. He should instead be taking the percentage of the 45 oz box.

**Work Time**

# 10% More

Huey, Dewey, and Louie see lemonade crystals at the store. Next to the regular size is a “bonus box.”

Huey says: "The '10% more' statement on the bonus box is NOT accurate. There is really more than 10% more."

Dewey says: "The '10% more' statement is NOT accurate. There is actually only 5% more, since 50 − 45 = 5."

Louie says: "The '10% more' statement IS accurate, since 10% of 50 is 5."

Only one of the boys is correct.

- Decide who is correct and show, mathematically, why he is correct.
- Say what mistakes you think each of the other two boys made.

# Free Space

# Answers

- Since 0.45 > 0.4, the 1.5-gigabyte disk has more free space than the 2-gigabyte disk.
For the 2-gigabyte disk: 100% – 80% = 20% free space.

0.2(2.0) = 0.4 gigabytes of free space.

For the 1.5-gigabyte disk: 100% – 70% = 30% free space.

0.3(1.5) = 0.45 gigabytes of free space.

**Work Time**

# Free Space

Irwin has a computer with two hard disks.

One is a 2-gigabyte disk that is 80% full.

The second is a 1.5-gigabyte disk that is 70% full.

- Which disk has more free space?
- Justify your answer mathematically.