Envision Math Accelerated Grade 7 Volume 1 Chapter 4 Analyze And Solve Percent Problems
Question. The florist uses purple and white flowers in the ratio of 3 purple flowers to 1 white flower.
Given:
The florist uses purple and white flowers in the ratio of 3 purple flowers to 1 white flower.
The florist uses purple and white flowers in a ratio of 3: 1.
That means there are 4 flowers in 1 arrangement.
He needs to make 30 identical arrangements.
⇒ 30⋅4 = 120
⇒ 30.3: 30.1
⇒ 90: 30
The florist will need 120 flowers for 30 identical arrangements. He will need 90 purple flowers and 30 white flowers.
The florist will need 120 flowers for 30 identical arrangements. He will need 90 purple flowers and 30 white flowers.
It is given that purple and white flowers are in the ratio of 3 purple flowers to 1 white flower.
That means that the purple flower will be related to the white flowers in a ratio of 3:1.
This means if there are 3 white flowers, we will require 9 purple flowers.
Purple will be 3 times the number of white flowers.
Purple flowers are 3 times the number of white flowers.
Question. The florist can only buy white flowers that have 3 white flowers and 2 red flowers.
Given:
The florist can only buy white flowers that have 3 white flowers and 2 red flowers.
He needs 90 out of 120 white flowers.
⇒ 90 ÷ 3 = 30
⇒ 30 ÷ 2 = 60
He has to buy 30 groups (2 red in every group).
The florist have to buy 60 red flowers, for 30 groups, 2 red flowers for every group.
Percent is the rate, number or amount in each hundred.
A fraction is a ratio or quantity which is not a whole number.
Fractions and percent can represent the same number just differently.
They are equivalent and that is a proportional relationship.
Percent and fractions can represent the same numbers (can be proportional).
Question. Camila makes 2 of her 5 shots attempted. Find the percent for Camila and then compare with Emily’s.
Given:
Camila makes 2 of her 5 shots attempted.
We find the percent for Camila and then compare with Emily’s.
\(\frac{2}{5}=\frac{p}{100}\)
0.4 = \(\frac{p}{100}\)
p = 40%
Camila made 40% of her shots. Camila’s percent of the shots made is less than Emily’s.
Camila made 40% of her shots. Camila’s percent of the shots made is less than Emily’s.
Question. Megan’s room is expanded so the width is 150% of 3 meters.
Given:
Megan’s room is expanded so the width is 150% of 3 meters.
We find the width of the room:
\( \frac{w}{3}\) = \( \frac{150}{100}\)
w = \(\frac{450}{100}\)
w = 450
The new width of the room is 4.5 meters.
The new width of Megan’s room is 4.5 meters.
Given:
45% of iron per 8 mg.
We find the amount of iron needed each day:
\(\frac{8}{x}=\frac{45}{100}\)
\(\frac{800}{45} \)
x = 17.8
Therefore, the amount of iron required each day is 17.8mg.
The amount of iron required each day is 17.8 mg.
Percent is the rate, number or amount in each hundred.
A fraction is a ratio or quantity which is not a whole number.
Fractions and percent can represent the same number just differently.
They are equivalent and that is proportional relationship.
Percent and fractions can represent the same numbers (can be proportional).
Given:
\(\frac{75}{x}=\frac{150}{100}\)We know that \(\frac{150}{100}\) is 150% and it is greater than 1 whole.
So \(\frac{75}{x}\) must be greater too.
That means that w must be less than 75.
Therefore, w must be less than 75.
Given:
We know that
\(\frac{68}{100}=\frac{17}{x}\)x = \(\frac{17 \cdot 100}{68}\)
x = 25%
The percent proportion for the given bar diagram is 25%.
Therefore, the percent for the given bar diagram is 25%.
Question. Gia researches online that her car is worth $3,000. She hopes to sell it for 85% of that value, but she wants to get at least 70%. Find whether she get what she wanted or not.
Given that, Gia researches online that her car is worth $3,000.
She hopes to sell it for 85% of that value, but she wants to get at least 70%.
She ends up selling it for $1,800.
We need to find whether she get what she wanted or not.
Finding the 85 %, we get
\(\frac{85}{100}\)×3000
= 85 × 30
= 2550
Finding the 70 %, we get
\(\frac{70}{100}\)×3000
= 70 × 30
= 2100
But she got only $1800
She got less than what she wanted.
Question. The rabbit population in a certain area is 200% of last year’s population. There are 1100 rabbits this year. Find the number of rabbits there would be in the last year.
The rabbit population in a certain area is 200% of last year’s population.
There are 1100 rabbits this year.
We have to find the number of rabbits there would be in the last year.
The population of the rabbit is 200% in the last year.
While the number of rabbits in this year are 1100.
We will equate the number of rabbits to its percentage to calculate the number of rabbits in last year.
The calculation will be
\(\frac{1100}{w}=\frac{200}{100}\) \(\frac{1100}{w} \cdot w=\frac{200}{100} \cdot w\) \(1100 \cdot \frac{100}{200}=\frac{200 w}{100} \cdot \frac{100}{200}\) \(w=1100 \cdot \frac{100}{200}\)w = 550
Therefore, the number of rabbits last year is 550.
There were 550 rabbits present last year.
Question. There is a company that makes hair-care products had 3000 people try a new shape. It is given that of the 3000 people, 9 had a mild allergic reaction. Find the percent of people who had a mild allergic reaction.
There is a company that makes hair-care products had 3000 people try a new shape.
It is given that of the 3000 people, 9 had a mild allergic reaction.
We have to find the percent of people who had a mild allergic reaction.
There are 3000 people who had hair care products.
Among those 3000 people, 9 of them had allergic reactions.
The ratio of people who had allergic reactions is \(\frac{9}{100}\).
To find the percent from the ratio, we evaluate as below:
\(\frac{9}{3000}=\frac{p}{100}\) \(\frac{9}{3000} \cdot 100=\frac{p}{100} \cdot 100\) \(p=\frac{9}{3000} \cdot 100\)p = 0.3
The percent of people who had a mild allergic reaction is 0.3.
Question. There is a survey given about who owned which type of car. Find the percent of people who were completely satisfied with the car.
There is a survey given about who owned which type of car.
We have to find the percent of people who were completely satisfied with the car.
A survey is given regarding people who owned different types of cars.
In the car satisfaction survey, 1100 people were completely satisfied with their car.
740 people were somewhat satisfied while 160 are not at all satisfied.
We have to find the percent of people who were completely satisfied.
The total number of people who were surveyed are
1100 + 740 + 160 = 2000
To find the percent, we evaluate as below:
\(\frac{p}{100}=\frac{1100}{2000}\) \(\frac{p}{100}=\frac{1100}{2000}\) \(p=\frac{1100}{2000} \cdot 100\)p = 55
The percent of people who were completely satisfied with their type of car is 55%.
Question. The Washington’s buy a studio apartment for $240000. They pay a down payment of $60000. Find that their down payment is what percent of the purchase price.
It is given that the Washington’s buy a studio apartment for $240000. They pay a down payment of $60000.
We have to find that their down payment is what percent of the purchase price.
The Washington’s buy a studio apartment for $240000.
They pay a down payment for the studio apartment is $60000.
We have to find that what percent of purchase price is of their down payment.
To find the percent, we evaluate as below:
\(\frac{60000}{240000}=\frac{p}{100}\) \(\frac{60000}{240000} \cdot 100=p\) \(p=\frac{60000}{240000} \cdot 100\)p = 25
Their down payment is 25% percent of the purchase price.
It is given that the Washington’s buy a studio apartment for $240000. They pay a down payment of $60000.
We have to find that what percent of purchase price would be of a $12000 down payment.
The Washington’s buy a studio apartment for $240000.
They pay a down payment for the studio apartment is $60000.
We have to find that what percent of purchase price what percent of purchase price would be of a $12000 down payment.
To find the percent, we evaluate as below:
\(\frac{12000}{240000}=\frac{p}{100}\) \(\frac{12000}{240000} \cdot 100=p\) \(p=\frac{12000}{240000} \cdot 100\)p = 5
The percent of the purchase price would a $12000 down payment be is 5%.
Question. A restaurant customer left $3.50 as a tip. The tax on the meal was 7% and the tip was 20% of the cost including tax. Find that what information is not necessary to calculate the bill.
It is given that a restaurant customer left $3.50 as a tip.
The tax on the meal was 7% and the tip was 20% of the cost including tax.
The tip left by the customer at a restaurant is $3.50.
They percentage of tax on the meal was 7 % and of the tip it was 20% of the cost including the tax.
We have to find that what information is not necessary to calculate the bill.
For computing the bill, we do not need to include the tax.
The tax is not needed to compute the bill.
It is given that a restaurant customer left $3.50 as a tip.
The tax on the meal was 7% and the tip was 20% of the cost including tax.
The tip left by the customer at a restaurant is $3.50.
They percentage of tax on the meal was 7 % and of the tip it was 20% of the cost including the tax.
We have to find the amount of total bill.
For computing the bill, we will calculate as below:
\(\frac{20}{100}=\frac{3.5}{x}\) \(\frac{20}{100} \cdot x=\frac{3.5}{x} \cdot x\) \(\frac{20 x}{100} \cdot \frac{100}{20}=3.5 \cdot \frac{100}{20}\)x = 17.5
To get the total bill, we will also have to add the tip left by the customer.
17.5+3.5=21
The total bill of the customer in the restaurant is $21.
Question. Find the estimate for 380% of 60.
We have to find the estimate for 380% of 60.
The estimate for 380% of 60 will be evaluated as below:
\(\frac{380}{100}=\frac{x}{60}\) \(\frac{380}{100} \cdot 60=\frac{x}{60} \cdot 60\) \(x=\frac{380}{100} \cdot 60\)x = 228
Therefore, the estimate is approximately 228.
The estimate for 380% of 60 will be 228.
Question. Marna thinks that about 35% of her mail is junk mail. She gets twice as much regular mail as junk mail. Verify whether the statement is correct or not.
Marna thinks that about 35% of her mail is junk mail.
She gets twice as much regular mail as junk mail.
We have to verify whether the statement is correct or not.
Marna gets twice as much regular mail as junk mail. So, the ratio of regular mail to junk mail is 2 is to 1.
Thus, if we consider the total mail as 100%, the ratio of both will be represented as
2:1=\(66.\overline{6}\) :\(33.\overline{3}\)
But, Marna thinks that she gets 35% mail as junk mail.
Which is not true, because actually, she gets \(33.\overline{3}\) of junk mail.
Therefore, she is not correct.
Marna’s statement is not correct because she gets around \(33.\overline{3}\) of junk mail and not 35%.
Question. Hypatia has read 13 chapters of a book. The book contains total 22 chapters. Find the percent of the chapters she has read.
It is given that Hypatia has read 13 chapters of a book.
The book contains total 22 chapters.
We have to find the percent of the chapters she has read.
The book has 22 chapters and Hypatia has read 13 of them.
The ratio of the chapters she has read will be \(\frac {13}{22}\).
So, the percent of chapters she has read will be
\(\frac{13}{22}=\frac{x}{100}\) \(\frac{13}{22} \cdot 100=\frac{x}{100} \cdot 100\) \(x=\frac{13}{22} \cdot 100\) \(x=59 . \overline{09}\)
The percentage of the chapters Hypatia has read is\(59 . \overline{09}\)
Question. A survey found that 27% of high school students and 94% of teachers and school employees drive to school.
A survey found that 27% of high school students and 94% of teachers and school employees drive to school.
The ratio of students to employees is about 10 to 1.
Roger states that the number of students who drive to school is greater than the number of teachers and employees who drive to school.
We have to tell how Roger’s statement could be correct.
The information gained by the survey is that 27% of high school students and 94% of teachers and school employees drive to school.
The ratio of the students to employees is 10:1.
We express the ratio as 10:1 = 1000:100
We evaluate the percentages we get:
\(\frac{27}{100} \cdot 1000\) = 270
\(\frac{94}{100} \cdot 100\) = 94
Thus, if we count the teachers as employees then, Roger’s statement is right.
Roger’s statement is correct if we count the teachers as employees.
Question. Stefan sells Jin a bicycle for $114 and a helmet for $18. The total cost for Jin is 120% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally?
Given:
Stefan sells Jin a bicycle for $114 and a helmet for $18.
The total cost for Jin is 120% of what Stefan spent originally to buy the bike and helmet.
How much did Stefan spend originally?
To find/solve
How much money did he make by selling the bicycle and helmet to Jin?
\(\frac{120}{100}=\frac{132}{?}\) \(\frac{120}{100} \cdot ?=\frac{132}{?} \cdot ?\) \(\frac{120}{100} \cdot \frac{100}{120}=132 \cdot \frac{100}{120} ?\)? = 110
First, multiply both sides by the variable and then by the reciprocal.
110
He make 110 by selling the bicycle and helmet to Jin.
Question. This month you spent 140% of what you spent last month. Last month you spent $30. How much did you spend this month?
Given:
Last month you spent $30.
This month you spent 140% of what you spent last month.
Set up a proportion to model this situation.
To find/solve
How much did you spend this month?
\(\frac{140}{100}=\frac{?}{30}\) \(\frac{140}{100} \cdot 30=\frac{?}{30} \cdot 30\) \(?=30 \cdot \frac{140}{100}\)? = 42
First, multiply both sides by the variable and then by the reciprocal.
42
The amount spends this month is 42.
Question. The owner of a small store buys coats for $50.00 each. She sells the coats for $90.00 each find percent of the purchase price is the selling price?
Given:
The owner of a small store buys coats for $50.00 each.
She sells the coats for $90.00 each
To find/solve
What percent of the purchase price is the selling price?
\(\frac{90}{50}=\frac{?}{100}\) \(\frac{90}{50} \cdot 100=\frac{?}{100} \cdot 100\) \(?=100 \cdot \frac{90}{50}\)? = 180
First, multiply both sides by the variable and then by the reciprocal.
180
180 percent of the purchase price is the selling price.
Given:
The owner of a small store buys coats for $50.00 each.
The owner increases the sale price the same percent that you found in Part A when she buys jackets for $35 and sells them.
To find/solve
How many jackets must the owner buy for the total jacket sales to be at least $250?
\(\frac{180}{100}=\frac{?}{35}\) \(\frac{180}{100} .35=\frac{?}{35} .35\) \(?=35 \cdot \frac{180}{100}\)? = 63
250 ÷ 63 = 3.97
3.97 ≈ 4
First, multiply both sides by the variable and then by the reciprocal.
4
4 jackets must the owner buy for the total jacket sales to be at least $250.