Percentage - SAT Math
Card 0 of 20
When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?
When y is decreased by ten percent, the result is equal to fifteen percent of x. Assuming both x and y are nonzero, what is the ratio of x to y?
The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.
If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.
Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.
Now, we set these two expressions equal to one another.
(9/10)y = (3/20)x
Multiply both sides by 20 to eliminate fractions.
18_y_ = 3_x_
The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.
18_y_ = 3_x_
Divide both sides by 3.
6_y_ = x
Divide both sides by y.
6 = x/y
Thus, the ratio of x to y is 6.
The answer is 6.
The problem states that decreasing y by ten percent gives us the same thing as taking fifteen percent of x. We need to find an expression for decreasing y by ten percent, and an expression for fifteen percent of x, and then set these two things equal.
If we were to decrease y by ten percent, we would be left with ninety percent of y (because the percentages must add to one hundred percent). We could write ninety percent of y as 0.90_y_ = (90/100)y = (9/10)y. Remember, when converting from a percent to a decimal, we need to move the decimal two places to the left.
Similarly, we can write 15% of x as 0.15_x_ = (15/100)x = (3/20)x.
Now, we set these two expressions equal to one another.
(9/10)y = (3/20)x
Multiply both sides by 20 to eliminate fractions.
18_y_ = 3_x_
The question asks us to find the ratio of x to y, which is equal to x/y. Thus, we must rearrange the equation above until we have x/y by itself on one side.
18_y_ = 3_x_
Divide both sides by 3.
6_y_ = x
Divide both sides by y.
6 = x/y
Thus, the ratio of x to y is 6.
The answer is 6.
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Write 7.5% as a fraction.
Write 7.5% as a fraction.
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
First convert the percentage to a decimal:
7.5% = .075
Then turn this into a fraction:
.075 = 75/1000
Simplify by dividing the numerator and denominator by 25:
75/1000 = 3/40
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Write as a fraction: 22%
Write as a fraction: 22%
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
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25% of 64 is equal to 5% of what number?
25% of 64 is equal to 5% of what number?
25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
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Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Compare your answer with the correct one above
Turn the following percentage into a fraction:
Turn the following percentage into a fraction:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
Since a percentage is a "part of 100" to turn it into a fraction we take the original number in the percent and place it over 100:
From here, simplify the fraction as necessary:
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What is the fractional equivalent to 30% of a given a is 12.
What is the fractional equivalent to 30% of a given a is 12.
First write the question out in equation form.
Since the question states that
the equation becomes,
.
From here, convert 30% into a fraction.
Substituting the fraction in for the percentage the equation becomes,
First write the question out in equation form.
Since the question states that
the equation becomes,
From here, convert 30% into a fraction.
Substituting the fraction in for the percentage the equation becomes,
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The cost of manufacturing a single teddy bear is $6.25. A teddy bear company sells 200 bears for $1750. What is the profit percentage per single bear?
The cost of manufacturing a single teddy bear is $6.25. A teddy bear company sells 200 bears for $1750. What is the profit percentage per single bear?
First we must find out what the price is for one teddy bear, manufactured by this company. Thus we divide 1750 by 200 and find that each bear costs $8.75. To find out the profit per bear, we divide 8.75 by 6.25 to arrive at 1.4. The bears are thus sold for 140% of what it costs to make them, giving a 40% profit.
First we must find out what the price is for one teddy bear, manufactured by this company. Thus we divide 1750 by 200 and find that each bear costs $8.75. To find out the profit per bear, we divide 8.75 by 6.25 to arrive at 1.4. The bears are thus sold for 140% of what it costs to make them, giving a 40% profit.
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A craftsman builds a cabinet. He pays $250 to buy the wood and miscellaneous materials for the cabinet. He spends 20 hours building the cabinet. If he values his time at $40 per hour and expects a profit margin of 50% above labor and materials, how much should he charge for the cabinet?
A craftsman builds a cabinet. He pays $250 to buy the wood and miscellaneous materials for the cabinet. He spends 20 hours building the cabinet. If he values his time at $40 per hour and expects a profit margin of 50% above labor and materials, how much should he charge for the cabinet?
Total Cost = Material Cost + Labor Cost + Profit
Labor Cost = $40/hour * 20 hours = $800
Profit Margin of 50% = Cost x 0.50 = $1050 x 0.50 = $525
Total Cost = $250 + $800 + $525 = $1575
Total Cost = Material Cost + Labor Cost + Profit
Labor Cost = $40/hour * 20 hours = $800
Profit Margin of 50% = Cost x 0.50 = $1050 x 0.50 = $525
Total Cost = $250 + $800 + $525 = $1575
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Each wooden chair that a carpenter makes requires $20 worth of supplies. He then sells the chairs for $50 each. The carpenter recently discovered a new supplier that would allow him to spend 25% less on supplies. If he doesn't change his selling price, by what percent could the carpenter increase his profit by using the new supplier?
Each wooden chair that a carpenter makes requires $20 worth of supplies. He then sells the chairs for $50 each. The carpenter recently discovered a new supplier that would allow him to spend 25% less on supplies. If he doesn't change his selling price, by what percent could the carpenter increase his profit by using the new supplier?
Using $20 worth of supplies and selling the chairs for $50 each, the carpenter is originally making a profit of $30 per chair.
The new supplier would reduce costs by 25% or 1/4. One-fourth of $20 is $5, so the new supplier would be $5 less, or $15.
If the selling price is the same ($50), then the carpenter would now make a profit of $35 per chair, a change of $5.
To calculate percent increase, divide the actual change in profit by the original profit amount, and multiply the result by 100%:
(Actual Change ÷ Original Amount) * 100% = 5/30 * 100% = 500%/30 = 16.7%
Using $20 worth of supplies and selling the chairs for $50 each, the carpenter is originally making a profit of $30 per chair.
The new supplier would reduce costs by 25% or 1/4. One-fourth of $20 is $5, so the new supplier would be $5 less, or $15.
If the selling price is the same ($50), then the carpenter would now make a profit of $35 per chair, a change of $5.
To calculate percent increase, divide the actual change in profit by the original profit amount, and multiply the result by 100%:
(Actual Change ÷ Original Amount) * 100% = 5/30 * 100% = 500%/30 = 16.7%
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