QuestionFind the percentage by which the first number is greater than the second, given they are $30\%$ and $40\%$ less than a third number.

Studdy Solution

STEP 1

Assumptions1. Let the third number be x. . The first number is30% less than x.
3. The second number is40% less than x.
4. We need to find the percentage by which the first number is more than the second.

STEP 2

First, let's express the first and second numbers in terms of x.The first number is30% less than x, so it is70% of x.The second number is40% less than x, so it is60% of x.
$First\, number =0.7x$ $Second\, number =0.6x$

STEP 3

We need to find the percentage by which the first number is more than the second. This can be calculated by subtracting the second number from the first number, dividing by the second number, and then multiplying by100 to get the percentage.
$Percentage = \frac{First\, number - Second\, number}{Second\, number} \\times100\%$

STEP 4

Substitute the expressions for the first and second numbers into the equation.
$Percentage = \frac{0.7x -0.6x}{0.6x} \\times100\%$

STEP 5

implify the equation to find the percentage.
$Percentage = \frac{0.1x}{0.x} \\times100\%$

STEP 6

The x's cancel out, leaving us with $Percentage = \frac{0.1}{0.6} \\times100\%$

STEP 7

Calculate the percentage.
$Percentage = \frac{1}{6} \\times100\% =16 \frac{2}{3} \%$ So, the first number is $16 \frac{2}{3} \%$ more than the second number.

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QuestionFind the percentage by which the first number is greater than the second, given they are $30\%$ and $40\%$ less than a third number.

Studdy Solution

STEP 1

Assumptions1. Let the third number be x. . The first number is30% less than x.
3. The second number is40% less than x.
4. We need to find the percentage by which the first number is more than the second.

STEP 2

First, let's express the first and second numbers in terms of x.The first number is30% less than x, so it is70% of x.The second number is40% less than x, so it is60% of x.
$First\, number =0.7x$ $Second\, number =0.6x$

STEP 3

STEP 4

Substitute the expressions for the first and second numbers into the equation.
$Percentage = \frac{0.7x -0.6x}{0.6x} \\times100\%$

STEP 5

implify the equation to find the percentage.
$Percentage = \frac{0.1x}{0.x} \\times100\%$

STEP 6

The x's cancel out, leaving us with $Percentage = \frac{0.1}{0.6} \\times100\%$

STEP 7

Calculate the percentage.
$Percentage = \frac{1}{6} \\times100\% =16 \frac{2}{3} \%$ So, the first number is $16 \frac{2}{3} \%$ more than the second number.

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QuestionFind the percentage by which the first number is greater than the second, given they are 30%30\%30% and 40%40\%40% less than a third number.

Studdy Solution

STEP 1

Assumptions1. Let the third number be x. . The first number is30% less than x.3. The second number is40% less than x.4. We need to find the percentage by which the first number is more than the second.

STEP 2

First, let's express the first and second numbers in terms of x.The first number is30% less than x, so it is70% of x.The second number is40% less than x, so it is60% of x.First number=0.7xFirst\, number =0.7xFirstnumber=0.7xSecond number=0.6xSecond\, number =0.6xSecondnumber=0.6x

STEP 3

STEP 4

Substitute the expressions for the first and second numbers into the equation.Percentage=0.7x−0.6x0.6xtimes100%Percentage = \frac{0.7x -0.6x}{0.6x} \\times100\%Percentage=0.6x0.7x−0.6x​times100%

STEP 5

implify the equation to find the percentage.Percentage=0.1x0.xtimes100%Percentage = \frac{0.1x}{0.x} \\times100\%Percentage=0.x0.1x​times100%

STEP 6

The x's cancel out, leaving us withPercentage=0.10.6times100%Percentage = \frac{0.1}{0.6} \\times100\%Percentage=0.60.1​times100%

STEP 7

Calculate the percentage.Percentage=16times100%=1623%Percentage = \frac{1}{6} \\times100\% =16 \frac{2}{3} \%Percentage=61​times100%=1632​%So, the first number is 1623%16 \frac{2}{3} \%1632​% more than the second number.

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QuestionFind the percentage by which the first number is greater than the second, given they are $30\%$ and $40\%$ less than a third number.

Assumptions1. Let the third number be x. . The first number is30% less than x.
3. The second number is40% less than x.
4. We need to find the percentage by which the first number is more than the second.

First, let's express the first and second numbers in terms of x.The first number is30% less than x, so it is70% of x.The second number is40% less than x, so it is60% of x.
$First\, number =0.7x$ $Second\, number =0.6x$

Substitute the expressions for the first and second numbers into the equation.
$Percentage = \frac{0.7x -0.6x}{0.6x} \\times100\%$

implify the equation to find the percentage.
$Percentage = \frac{0.1x}{0.x} \\times100\%$

The x's cancel out, leaving us with $Percentage = \frac{0.1}{0.6} \\times100\%$

Calculate the percentage.
$Percentage = \frac{1}{6} \\times100\% =16 \frac{2}{3} \%$ So, the first number is $16 \frac{2}{3} \%$ more than the second number.