Master Percent Proportion and Equation, Understand Percent of Change

Absolute Error	Relative Error	Percent Error
$∣ 480 - 400 ∣ = 80$	$\frac{8 0}{4 0 0} = 0.2$	$0.2 \cdot 100 % = 20 %$

Absolute Error

Relative Error

Percent Error

∣ 480 - 400 ∣ = 80

\frac{8 0}{4 0 0} = 0.2

0.2 \cdot 100 % = 20 %

Mark decides to go on an

8 -

hour road trip. At the start, his phone's battery charge is at

60 % .

In normal usage, his battery lasts

15

hours at full charge. Determine if Mark will be able use his phone from the start to the end of the trip.

Note that 15 hours represents 100 % of the battery. Since it is told that Mark's battery charge at 60 % now, we can calculate 60 % of 15 hours to see how many hours are left. Let's write this situation as an equation by using the percent equation. a= p % * w In this equation, a represents the part, p % represents the percent, and w represents the whole. Let's substitute our values into the percent equation. a= 60 % * 15 We will now solve this equation for the value of a.

Since Mark's trip will take 8 hours and his phone's battery will last 9 hours, we can say that yes, he can use his phone during the whole trip.

A medicine company conducted an experiment on $2500$ voluntary people about the effects of a new medicine. The results show that of the $2500$ people, $10$ had a mild allergic reaction to this new medicine.

Find the percent of the people that have a mild allergic reaction.

We are given that 10 out of the 2500 people that tried a new medicine had a mild allergic reaction. We want to find out what percent of the people had a mild allergic reaction. Let's start by drawing a bar diagram to represent the problem.

Next, we will write a percent proportion to find the percent. a/w=p/100 Note that a is the number of people with a mild allergic reaction and w is the total number of people. With this in mind, now substitute our values into the percent proportion. 10/2500=p/100 Note that we got an equation that we can solve for p. We will multiply both sides of the equation by 100 to get the percent value p alone.

We found that p=0.4. This means that 0.4 % of the people had a mild allergic reaction to the new medicine.

In the following figure, each grid is the same size.

What percent of the figure is drawn as green? Round the answer to the nearest integer.

We have been asked to establish the percent of the image is green. In other words, we want to know what percent of all of the squares are green squares. We will represent it by a percent equation. p % * b = a Here, b represents the whole which is the total number of squares and a is the part which is the total number of green squares.

As we can see, there are b=5 * 14 = 70 squares in total and a= 19 green squares in total. Now we can substitute these values into the percent equation and solve it for p.

We can conclude that about 27 % of the figure is green.

Mark uses a bar graph to display the results of a survey that asks several students to vote on a new candidate who will represent the school in a national dance festival.

However, Mark forgot to write the scale labels.

Find the percent of the votes that the most popular candidate received.

If there are

240

votes in total, how many votes does candidate C receive?

Note that the vertical axis is related to votes that each candidate received. However, there are no scale labels, except for the 0 one.

Without the scale we cannot tell how many votes each candidate received. However, we know that the number of lines each bar intersects tells how many portions of votes each candidate received. Let's count how many lines intersect the bars.

Next, let's add the found numbers to find how many overall portions of votes there were. 1+7+3+5+4 = 20 Notice that the most popular candidate, who is B, received 7 votes. Now that we also know the total portion of the votes, we can calculate the percent of the votes for the most popular candidate by using the percent equation. a=p % * w Recall that a represents the part which is the most popular candidate's portion of the votes, p is the percent, and w is the whole which represents the overall portions of the votes. With these in mind, let's substitute the obtained values into the percent equation.

We can conclude that the most popular candidate, who is candidate B, received 35 % of the votes.

Now, we assume that there are 240 votes total. We want to find how many votes are for candidate C. Recall the graph from the previous part in which we counted the number of tick lines each bar intersects.

From Part B we know that overall there are 20 portions of votes and 3 of them are votes for candidate C. Let's find the amount of percent of the votes that candidate C received by using the percent equation. a=p % * w ⇓ 3=p % * 20 Let's solve this equation!

We found that candidate C received the 15 % of the total number of votes. Now, let's calculate 15 % of 240.

This means that the candidate C received 36 votes.

The table shows the geometry scores of Mark in four tests. Mark needs to get $70 %$ of the total test points to pass the course.

Test Score	Point Value
$79 %$	$200$
$82.5 %$	$100$
$55 %$	$80$
$?$	$50$

According to this table, what is the score that Mark needs on the last test to be able to pass the course?

We want to determine the score on the last test for which Mark earns 70 % of the total points on the tests. We can use this information to write the percent equation for the total number of points scored. Total Points Scored= 70 %( Total Point Value) Now, we can consider the given table.

Test Score	Point Value
79 %	200
95.5 %	100
55 %	80
?	50

First, we can use the table to calculate the number of points scored on each test. We can do so by multiplying the test score by the point value for each test. Remember that we can represent the score on the last test with an arbitrary variable a.

Test Score	Point Value	Points Scored
79 %	200	79 %* 200 = 158
82.5 %	100	82.5 %* 100 = 82.5
55 %	80	55 %* 80 = 44
a %	50	a %* 50 = 0.5a

Now, we can calculate the sum of all point values and the sum of points scored in each test.

Test Score	Point Value	Points Scored
79 %	200	79 %* 200 = 158
82.5 %	100	82.5 %* 100 = 82.5
55 %	80	55 %* 80 = 44
a %	50	a %* 50 = 0.5a
Sum	= 430	= 284.5+0.5a

Finally, we can substitute the values in our equation. Total Points Scored= 70 %( Total Point Value) ⇕ 284.5+0.5a= 70 % * 430 Now, we can solve the equation for a.

We found that Mark must get 301 in total from all four tests. Next, we will subtract 284.5 from both sides of the equation.

Finally, we will divide both sides of the equation by 0.5 to get the variable a alone.

Mark needs to score 33 % on the last test to be able to pass the course.

Increase	New amount $>$ Original amount
Decrease	Original amount $>$ New amount

The Percent Proportion and Equation, and Percent of Change

Catch-Up and Review

Paying a Loan

Writing the Percent as a Ratio

Percent Proportion

Finding the Percent of Toys

Hint

Solution

Solving a Percent Proportion

Using the Percent in an Equation

Percent Equation

Arranging the Toys According to Age Groups

Hint

Solution

Solving a Percent Equation

Expressing the Change as a Percent

Percent of Change

Calculating Percent of Change

Calculating the Change as a Percent

Hint

Solution

Calculating the Percent of Change

Expressing the Error as a Percent

Relative Error and Percent Error

Estimating a Wrong Price

Hint

Solution

Calculating the Percent of Change for a Loan

Hint

Solution

Extra

The Percent Proportion and Equation, and Percent of Change

Recommended exercises

	15 Theory slides
	12 Exercises - Grade E - A
	Each lesson is meant to take 1-2 classroom sessions