Envision Math Accelerated Grade 7 Volume 1 Chapter 4 Analyze And Solve Percent Problems
Question. Jaime’s older brother and his three friends want to split the cost of lunch. They also want to leave a 15-20% tip. Determine how much should each person pay.
Given that, Jaime’s older brother and his three friends want to split the cost of lunch. They also want to leave a 15−20 % tip.
We need to determine how much should each person pay.
The total bill amount is $78
Finding the tip amount for each percentage given, we get:
\(\frac{15}{100} \times 78\) = 11.7
\(\frac{20}{100} \times 78\) = 1.56
Thus, the amount including the tip is somewhere between 78 + 11.7 = 89.7 and 78 + 15.6 = 93.6
Splitting the bill amount for each person, thus we get
\(\frac{89.7}{4} \) = 22.425
\(\frac{93.6}{4} \) = 23.4
Each person should pay somewhere in between $22.425 and $23.4
Question. Find which line on the receipt we have to use to calculate the tip.
We need to find which line on the receipt we have to use to calculate the tip.
The tip is usually calculated after the bill amount.
Here, the total bill amount is necessary to calculate the tip amount.
Therefore, from the given receipt
The last line i.e., the total will be used to calculate the tip.
We have to use the last line on the receipt to calculate the tip.
Question. Find the 0.08% of 720.
We need to find 0.08% of 720.
Finding the percentage, we get:
\(\frac{0.08}{100} \times 720\)= \(\frac{8}{10000} \times 720\)
= \(\frac{8}{1000} \times 72\)
= \(\frac{576}{1000}\)
= 0.576
The value is 0.576
We need to find 162.5% of 200.
Finding the percentage, we get:
\(\frac{162.5}{100} \times 200\)= 162.5×2
= 325
The value is 325
We need to find 0.3% of 60.
Finding the percentage, we get:
\(\frac{0.3}{100} \times 60\)= \(\frac{3}{1000} \times 60\)
= \(\frac{3}{100} \times 6\)
= \(\frac{18}{100}\)
= 0.18
The value will be 0.18
Question. Explain why 51% of a number is more than half of the number.
We need to explain why 51 % of a number is more than half of the number.
We know that half of the number means 50 % of the number.
Here, 51 % of the number means that it will be 1 % more than half.
For example, if the number is 200
Then the half of it will be
\(\frac{200}{2}\) = 100
Thus, 51 % of the number will be
= \(\frac{51}{100} \times 200\)
=51 × 2
=102
Thus, it will be more than half of the number.
51 % of a number is 1 % more than half of the number.
Question. How do the percents show the relationship between quantities.
We need to how do the percents show the relationship between quantities.
The percentage is also denoted as the ratio.
The ratio is nothing but the comparison between two same or different quantities.
The first term of the percent is often compared to the number 100.
For example, 35 % of shirts are sold denotes that out of 100 shirts, 35 has been sold out.
We can often denote the percent using the sign “%”.
A percent is a ratio in which the first term is compared to 100. It is used for comparing two quantities. Percents are used to calculate the amount of one thing compared to the other. Percents can be used to compare very small or very large quantities as a fraction of 100.
Question. Gene stated that finding 25% of a number is the same as dividing the number by \(\frac{1}{4}\). We need to determine whether Gene is correct or not.
Given that, Gene stated that finding 25 % of a number is the same as dividing the number by \(\frac{1}{4}\).
We need to determine whether Gene is correct or not.
25 % of a number is denoted by
\(\frac{25}{100}\)=\(\frac{1}{4}\)
Thus, when we divide the number by \(\frac{1}{4}\), it is the same as finding 25 % of the number.
For example, if the number is 200.
Thus, \(\frac{25}{100}\) × 200 = 25 × 2 = 50
Also, \(\frac{200}{4}\) = 50
= 50
The result is the same.
Therefore, Gene is correct.
Question. Find the percent of the 59% number of the 640.
We need to find the percent of the given number.
The given number is 59 % of the 640
Solving the given, we get:
\(\frac{59}{100}\) × 640
= \(\frac{59}{10}\) × 64
= \(\frac{3776}{10}\)
= 377.6
The answer is 377.6
We need to find the percent of the given number.
The given number is 0.20 % of the 3542
Solving the given, we get:
\(\frac{0.20}{100} \times 3542\)= \(\frac{708.4}{100}\)
= 7.084
The answer is 7.084
We need to find the percent of the given number.
The given number is 195 % of the 568
Solving the given, we get:
\(\frac{195}{100}\) × 568
= \(\frac{110760}{100}\)
= 1107.6
The value is 1107.6
We need to find the percent of the given number.
The given number is 74 % of the 920
Solving the given, we get:
\(\frac{74}{100}\) × 920
=\(\frac{68080}{100}\)
= 680.8
The value is 680.8
Question. Water is 2 parts hydrogen and 1 part oxygen (H2O). For one molecule of water, each atom has the atomic mass unit. Find what percent of the mass of a water molecule is hydrogen.
Given that, Water is 2 parts hydrogen and 1 part oxygen (H2O).
For one molecule of water, each atom has the atomic mass unit, u, shown.
We need to find what percent of the mass of a water molecule is hydrogen.
Finding the total mass, we get
16.00 + 1.01 + 1.01 = 18.02
We need to find what percent of the total mass is hydrogen.
\(\frac{x}{100}\) × 18.02 = 2.02
x × 18.02 = 2.02 × 100
x × 18.02 = 202
x = \(\frac{202}{18.02}\)
x = 11.2
The percent is 11.2 %
% percent of the mass of a water molecule is hydrogen.
Question. A local little league has a total of 60 players, 80% of whom are right-handed. Find how many right-handed players are there.
Given that, a local Little League has a total of 60 players, 80 % of whom are right-handed.
We need to find how many right-handed players are there.
Let x be the number of right-handed people, thus we get, using equivalent ratios we get
\(\frac{x}{60}\) × 60
= \(\frac{80}{60}\) × 60
x = \(\frac{80 \times 60}{100}\)
x = \(\frac{4800}{100}\)
x = 48
48 out of 60 players are right-handed.
Question. Sandra’s volleyball team has a total of 20 uniforms. Find how many uniforms are medium-sized.
Given that, Sandra’s volleyball team has a total of 20 uniforms.
20 % are medium-sized uniforms. We need to find how many uniforms are medium-sized.
Let x be the number of medium-sized uniforms, thus we get, using equivalent ratios we get
\(\frac{x}{20}\) × 20
= \(\frac{20}{100}\) × 20
x = \(\frac{400}{100}\)
x = 4
4 out of 20 uniforms are medium-sized.
Question. Meg is a veterinarian. In a given week, 50% of the 16 dogs she saw were Boxers. Steve is also a veterinarian. In the same week, 7 of the 35 dogs he saw this week were Boxers. Find which part Steve needs to find the part, the whole or the percent.
Given that, Meg is a veterinarian. In a given week, 50 % of the 16 dogs she saw were Boxers.
Steve is also a veterinarian. In the same week, 7 of the 35 dogs he saw this week were Boxers.
Each wants to record the part, the whole, and the percent.
We need to find which part Steve needs to find – the part, the whole, or the percent.
Finding the number of dogs Steve saw:
\(\frac{x}{100}\) = 7
x = 7 × \(\frac{100}{35}\)
x = \(\frac{700}{35}\)
x = \(\frac{100}{5}\)
x = 20
Thus, 20 % of dogs Steve saw. Thus, he needs to find the percent.
Steve needs to find the percent.
Question. The registration fee for a used car is 0.8% of the sale price of $5,700. Find the registration fee.
Given that, the registration fee for a used car is 0.8 % of the sale price of $5,700.
We need to determine the fee.
The registration fee is:
\(\frac{0.8}{100}\) × 5700
= 0.8 × 57
= 45.6
The registration fee is $45.6
Question. The total cost of an item is the price plus the sales tax. Find the sales tax to complete the table.
Given that, the total cost of an item is the price plus the sales tax.
We need to find the sales tax to complete the table.
Then find the total cost of the item.
Finding the sales tax of the item, we get:
\(\frac{4}{100}\) × 40
= \(\frac{160}{100}\)
= 1.6 dollars
The total price is calculated by adding selling price and sales tax.
Thus, we get
40 + 1.6 = 41.6 dollars
The sales tax is $1.6
The total price is $41.6
Question. Find whether 700% of 5 less than 10, greater than 10 but less than 100 or greater than 100.
We need to find whether 700 % of 5 less than 10, greater than 10 but less than 100 or greater than 100.
Solving the equation, we get:
\(\frac{700}{100}\) × 5
= 7 × 5
= 35
Thus the value is greater than 10 but less than 100.
The value obtained is 35 which is greater than 10 but less than 100.
Question. A new health drink has 130% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 45 mg. Find how many milligrams of vitamins are in the drink.
Given that, A new health drink has 130 % of the recommended daily allowance (RDA) for a certain vitamin.
The RDA for this vitamin is 45 mg.
We need to find how many milligrams of vitamins are in the drink.
Finding the vitamin amount of a new health drink, we get:
\(\frac{130}{100}\) × 45
= \(\frac{13}{10}\) × 45
= \(\frac{13}{2}\) × 9
= 58.5
58.5 mg of vitamins are in the drink.
Question. Brad says that if a second number is 125% of the first number, then the first number must be 75% of the second number. Find whether he is correct or not.
Given that, Brad says that if a second number is 125 % of the first number, then the first number must be 75 % of the second number.
We need to find whether he is correct or not.
Finding the percentage of the second number
Here, y be the second number and x be the first number.
Thus, we get:
\(\frac{125}{100}\) × x = y
x = y × \(\frac{100}{125}\)
x = y × \(\frac{4}{5}\)
x = y × 0.8
0.8 is equal to 80 %
Thus, the first number must be 80 % of the second number. Hence, he is incorrect.
Question. Mark and Joe work as jewelers. Mark has an hourly wage of $24 and gets overtime for every hour he works over 40 hours. The overtime pay rate is 150% of the normal rate. Joe makes 5% commission on all jewelry he sells. Find who earns more money in a week if Mark works 60 hours and Joe sells $21,000 worth of jewelry.
Given that, Mark and Joe work as jewelers. Mark has an hourly wage of $24 and gets overtime for every hour he works over 40 hours.
The overtime pay rate is 150 % of the normal rate. Joe makes 5 % commission on all jewelry he sells.
We need to find who earns more money in a week if Mark works 60 hours and Joe sells $21,000 worth of jewelry.
For Mark:
Find his overtime pay rate, thus we get:
x = \(\frac{150}{100}\) × 24
x = \(\frac{15}{5}\) × 12
x = 3 × 12
x = 36
Finding the total pay rate, we get:
20 × 36 = 720
40 × 24 = 960
Thus, the total is, 720 + 960 = 1680
Marks earns more money in a week.
Question. A forest covers 43,000 acres. A survey finds that 0.2% of the forest is old-growth trees. Find how many acres of old-growth trees.
Given that, A forest covers 43,000 acres.
A survey finds that 0.2 % of the forest is old-growth trees.
We need to find how many acres of old-growth trees are there.
Finding the acres of the forest which is old-growth trees, we get,
\(\frac{0.2}{100}\) × 43000
= 0.2 × 430
= 2 × 43
= 86
86 acres of old-growth trees are there.
Question. An Olympic-sized pool, which holds 660,000 gallons of water, is only 63% full. Find how many gallons of water are in the pool.
Given that, an Olympic-sized pool, which holds 660,000 gallons of water, is only 63 % full.
We need to find how many gallons of water are in the pool.
Finding the gallons of water are in the pool, we get
\(\frac{63}{100}\) × 660000
= 63 × 6600
= 415800
415800 gallons of water is in the pool.