Problem 1 :
The price of a product is increased from $25 to $30. Find the percent increase.
Problem 2 :
Find the percent decrease from 90 inches to 63 inches.
Problem 3 :
The price of a product is $30. If the price is increased by 15%, then find the new price.
Problem 4 :
The cost price of a product is $150 and it is sold at a loss of 30%. Find the selling price of the product.
Problem 5 :
John got 50% of the questions correct on a 40-question test and 80% on a 80-question test. What percent of all questions did John get correct?
Problem 6 :
The price of a dress is increased by 20%, then decreased by 40%, then increased by 25%. the final price is what percent of the original price.?
Problem 7 :
If x is 50% larger than z, and y is 20% larger than z, then x is what percent larger than y?
Problem 8 :
The number of students at a school decreased 20% from 2015 to 2016. If the number of students enrolled in 2016 was k, find the number of students enrolled in 2015 in terms of k.
Problem 9 :
Townsend Realty purchased a property for $140,000 after having received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Find the original price of the property (Round the answer to the nearest dollar).
Problem 10 :
Among 9th graders at a school, 30% of the students are Red Sox fans. Among those Red Sox fans, 40% are also Celtics fans. What percent of the 9th graders at the school are both Red Sox fans and Celtics fans?
Problem 1 :
The price of a product is increased from $25 to $30. Find the percent increase.
Solution :
Find the amount of change.
Amount of change = Greater value - Lesser value
= 30 - 25
= 5
Percentage change is
= (Amount of change / Original amount) x 100 %
= (5 / 25) ⋅ 100%
= 0.2 ⋅ 100 %
= 20 %
So, the percent increase from $25 to $30 is 20%.
Problem 2 :
Find the percent decrease from 90 inches to 63 inches.
Solution :
Find the amount of change.
Amount of change = Greater value - Lesser value
= 90 - 63
= 27
Percentage change is
= (Amount of change / Original amount) x 100 %
= (27 / 90) ⋅ 100%
= 0.3 ⋅ 100 %
= 30 %
So, the percent decrease from 90 inches to 63 inches is 30%.
Problem 3 :
The price of a product is $30. If the price is increased by 15%, then find the new price.
Solution :
The new price is
= (100 + 15)% of 30
= 115% ⋅ 30
= (115/100) ⋅ 30
= 1.15 ⋅ 30
= 34.5
So, the new price after 15% increase is $34.50
Problem 4 :
The cost price of a product is $150 and it is sold at a loss of 30%. Find the selling price of the product.
Solution :
Because the product is sold in loss, the cost price has to be decreased by 30% to find the selling price.
The selling price of the product is
= (100 - 30)% of 150
= 70% ⋅ 150
= (70/100) ⋅ 150
= 0.7 ⋅ 150
= 105
So, the selling price of the product is $105.
Problem 5 :
John got 50% of the questions correct on a 40-question test and 80% on a 80-question test. What percent of all questions did John get correct?
Solution :
Number of questions he got correct in 40-question test is
= 50% ⋅ 40
= 0.5 ⋅ 40
= 20
Number of questions he got correct in 80-question test is
= 80% ⋅ 80
= 0.8 ⋅ 80
= 64
Number of questions he got correct in both the tests is
= 20 + 64
= 84
Total number of questions in both the tests is
= 40 + 80
= 120
Percent of questions John got correct is
= (84/120) ⋅ 100%
= 70%
So, John got 70% of all questions correct.
Problem 6 :
The price of a dress is increased by 20%, then decreased by 40%, then increased by 25%. the final price is what percent of the original price.?
Solution :
Let $100 be the original price.
Price after 20% increase :
= (100 + 20)% ⋅ 100
= 120% ⋅ 100
= 1.2 ⋅ 100
= 120
Price after 40% decrease :
= (100 - 40)% ⋅ 120
= 60% ⋅ 120
= 0.6 ⋅ 120
= 72
Price after 25% increase :
= (100 + 25)% ⋅ 72
= 125% ⋅ 72
= 1.25 ⋅ 72
= 90
Original price is $100 and final price is $90.
So, the final price is 90% of the original price.
Problem 7 :
If x is 50% larger than z, and y is 20% larger than z, then x is what percent larger than y?
Solution :
Let z = 100
Finding the value of x :
x = (100 + 50)% ⋅ 100
x = 150% ⋅ 100
x = 1.5 ⋅ 100
x = 150
Finding the value of y :
y = (100 + 20)% ⋅ 100
y = 120% ⋅ 100
y = 1.2 ⋅ 100
y = 120
Difference between the value of x and y is
= 150 - 120
= 30
Percent change :
= (30 / 120) ⋅ 100 %
= 25 %
So, x is 25% larger than y.
Problem 8 :
The number of students at a school decreased 20% from 2015 to 2016. If the number of students enrolled in 2016 was k, find the number of students enrolled in 2015 in terms of k.
Solution :
Number of students enrolled in 2016 = k
Let x be the number of students enrolled in 2015.
Number of students enrolled in 2016 was decreased by 20% compared to 2015.
So, we have
Number of students enrolled in 2016 = (100 - 20)% ⋅ x
k = 80% ⋅ x
k = (80/100) ⋅ x
k = (4/5) ⋅ x
Multiply each side by 5/4.
(5/4) ⋅ k = x
1.25k = x
So, the number of students enrolled in 2015 is 1.25k.
Problem 9 :
Townsend Realty purchased a property for $140,000 after having received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Find the original price of the property (Round the answer to the nearest dollar).
Solution :
Let x be the original price of the property.
The price of the property after 40% discount :
= (100 - 40)% of x
= 60% ⋅ x
= 0.6x
The price of the property after additional 20% off :
= (100 - 20)% of 0.6x
= 80% ⋅ 0.6x
= 0.8 ⋅ 0.6x
= 0.48x
Therefore, the purchased price is 0.48x.
But, the purchased price given in the question is $140,000.
Then, we can have
0.48x = 140000
Divide each side by 0.32
x ≈ 291,667
So, original price of the property is about $291,667.
Problem 10 :
Among 9th graders at a school, 30% of the students are Red Sox fans. Among those Red Sox fans, 40% are also Celtics fans. What percent of the 9th graders at the school are both Red Sox fans and Celtics fans?
Solution :
Let 100 be the strength of 9th graders.
Number of Red Sox fans :
= 30% ⋅ 100
= 0.3 ⋅ 100
= 30
Number of Celtics and Red Sox fans :
= 40% ⋅ 30
= 0.4 ⋅ 30
= 12
Out of 100 students in 9th grade, 12 students are both Red Sox and Celtics fans.
So, 12% of the 9th graders are both Red Sox and Celtics fans.
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