QuestionIf $40\%$ of $a$ equals $80\%$ of $b$ , find what percent of $b$ is $a$ . A) $20\%$ B) $50\%$ C) $100\%$

Studdy Solution

STEP 1

Assumptions1. $40\%$ of $a$ equals $80\%$ of $b$ . We are asked to find what percent of $b$ is $a$

STEP 2

First, let's express the given equation in mathematical terms. $40\% \, of \, a =80\% \, of \, b$

STEP 3

Convert the percentages to decimal form.
$0.a =0.8b$

STEP 4

We are asked to find what percent of $b$ is $a$ . Let's express this as a fraction of $a$ over $b$ .
$\frac{a}{b} = ?$

STEP 5

To find the value of $\frac{a}{b}$ , we can rearrange the equation $0.4a =0.8b$ to solve for $\frac{a}{b}$ .
$\frac{a}{b} = \frac{0.8b}{0.4a}$

STEP 6

implify the equation by cancelling out the common factors.
$\frac{a}{b} = \frac{0.8}{0.4}$

STEP 7

Calculate the value of $\frac{a}{b}$ .
$\frac{a}{b} = \frac{0.}{0.4} =2$

STEP 8

Now, we know that $a$ is $2$ times $b$ . To express this as a percentage, we multiply by $100\%$ .
$a =2 \times b =200\% \, of \, b$ So, $a$ is $200\%$ of $b$ .

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QuestionIf $40\%$ of $a$ equals $80\%$ of $b$ , find what percent of $b$ is $a$ . A) $20\%$ B) $50\%$ C) $100\%$

Studdy Solution

STEP 1

Assumptions1. $40\%$ of $a$ equals $80\%$ of $b$ . We are asked to find what percent of $b$ is $a$

STEP 2

First, let's express the given equation in mathematical terms. $40\% \, of \, a =80\% \, of \, b$

STEP 3

Convert the percentages to decimal form.
$0.a =0.8b$

STEP 4

We are asked to find what percent of $b$ is $a$ . Let's express this as a fraction of $a$ over $b$ .
$\frac{a}{b} = ?$

STEP 5

To find the value of $\frac{a}{b}$ , we can rearrange the equation $0.4a =0.8b$ to solve for $\frac{a}{b}$ .
$\frac{a}{b} = \frac{0.8b}{0.4a}$

STEP 6

implify the equation by cancelling out the common factors.
$\frac{a}{b} = \frac{0.8}{0.4}$

STEP 7

Calculate the value of $\frac{a}{b}$ .
$\frac{a}{b} = \frac{0.}{0.4} =2$

STEP 8

Now, we know that $a$ is $2$ times $b$ . To express this as a percentage, we multiply by $100\%$ .
$a =2 \times b =200\% \, of \, b$ So, $a$ is $200\%$ of $b$ .

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QuestionIf 40%40\%40% of aaa equals 80%80\%80% of bbb, find what percent of bbb is aaa. A) 20%20\%20% B) 50%50\%50% C) 100%100\%100%

Studdy Solution

STEP 1

Assumptions1. 40%40\%40% of aaa equals 80%80\%80% of bbb . We are asked to find what percent of bbb is aaa

STEP 2

First, let's express the given equation in mathematical terms.40% of a=80% of b40\% \, of \, a =80\% \, of \, b40%ofa=80%ofb

STEP 3

Convert the percentages to decimal form.0.a=0.8b0.a =0.8b0.a=0.8b

STEP 4

We are asked to find what percent of bbb is aaa. Let's express this as a fraction of aaa over bbb.ab=?\frac{a}{b} = ?ba​=?

STEP 5

To find the value of ab\frac{a}{b}ba​, we can rearrange the equation 0.4a=0.8b0.4a =0.8b0.4a=0.8b to solve for ab\frac{a}{b}ba​.ab=0.8b0.4a\frac{a}{b} = \frac{0.8b}{0.4a}ba​=0.4a0.8b​

STEP 6

implify the equation by cancelling out the common factors.ab=0.80.4\frac{a}{b} = \frac{0.8}{0.4}ba​=0.40.8​

STEP 7

Calculate the value of ab\frac{a}{b}ba​.ab=0.0.4=2\frac{a}{b} = \frac{0.}{0.4} =2ba​=0.40.​=2

STEP 8

Now, we know that aaa is 222 times bbb. To express this as a percentage, we multiply by 100%100\%100%.a=2×b=200% of ba =2 \times b =200\% \, of \, ba=2×b=200%ofbSo, aaa is 200%200\%200% of bbb.

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QuestionIf $40\%$ of $a$ equals $80\%$ of $b$ , find what percent of $b$ is $a$ . A) $20\%$ B) $50\%$ C) $100\%$

Assumptions1. $40\%$ of $a$ equals $80\%$ of $b$ . We are asked to find what percent of $b$ is $a$

First, let's express the given equation in mathematical terms. $40\% \, of \, a =80\% \, of \, b$

Convert the percentages to decimal form.
$0.a =0.8b$

We are asked to find what percent of $b$ is $a$ . Let's express this as a fraction of $a$ over $b$ .
$\frac{a}{b} = ?$

To find the value of $\frac{a}{b}$ , we can rearrange the equation $0.4a =0.8b$ to solve for $\frac{a}{b}$ .
$\frac{a}{b} = \frac{0.8b}{0.4a}$

implify the equation by cancelling out the common factors.
$\frac{a}{b} = \frac{0.8}{0.4}$

Calculate the value of $\frac{a}{b}$ .
$\frac{a}{b} = \frac{0.}{0.4} =2$

Now, we know that $a$ is $2$ times $b$ . To express this as a percentage, we multiply by $100\%$ .
$a =2 \times b =200\% \, of \, b$ So, $a$ is $200\%$ of $b$ .