The original price of a shirt was $20. It was decreased to $15 . What is the percent decrease of the price of this shirt.
Solution to Problem 1:
The absolute decrease is
20 - 15 = $5
The percent decrease is the absolute decrease divided by the the original price (part/whole).
percent decease = 5 / 20 = 0.25
Multiply and divide 0.25 to obtain percent.
percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25%
Problem 2:
Mary has a monthly salary of $1200. She spends $280 per month on food. What percent of her monthly salary does she spend on food?
Solution to Problem 2:
The part of her salary that is spent on food is $280 out of her monthly salary of $1200
percent = part / whole = 280 / 1200 = 0.23 (rounded to 2 decimal places)
Multiply and divide 0.23 by 100 to convert in percent
percent = 0.23 * 100 / 100 = 23 / 100 = 23%
Problem 3:
The price of a pair of trousers was decreased by 22% to $30. What was the original price of the trousers?
Solution to Problem 3:
Let x be the original price and y be the absolute decrease. If the price was decreased to $30, then
x - y = 30
y is given by
y = 22% of x = (22 / 100) * x = 0.22 x
Substitute y by 0.22 x in the equation x - y = 30 and solve for x which the original price.
x - 0.22 x = 30
0.78 x = 30
x = $38.5
Check the solution to this problem by reducing the origonal price found $38.5 by 22% and see if it gives $30.
Problem 4:
The price of an item changed from $120 to $100. Then later the price decreased again from $100 to $80. Which of the two decreases was larger in percentage term?
Solution to Problem 4:
First decrease in percent
part / whole = (120 - 100) / 120 = 0.17 = 17%
Second decrease in percent
part / whole = (100 - 80) / 100 = 0.20 = 20%
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