Solved on Sep 03, 2023

The will divides the estate: $\frac{1}{4}$ to relatives, $\frac{3}{5}$ of the remaining to Charity A. What fraction of the estate goes to Charity A?

STEP 1

Assumptions1. The total estate is represented as1 (or100%) . $\frac{1}{4}$ of the estate is divided among relatives3. Of the remaining estate, $\frac{3}{5}$ goes to Charity A

STEP 2

First, we need to find the remaining estate after $\frac{1}{4}$ has been divided among relatives. We can do this by subtracting $\frac{1}{4}$ from1.
$Remaining\, estate = Total\, estate - Estate\, for\, relatives$

STEP 3

Now, plug in the given values for the total estate and the estate for relatives to calculate the remaining estate.
$Remaining\, estate =1 - \frac{1}{}$

STEP 4

Calculate the remaining estate.
$Remaining\, estate =1 - \frac{1}{4} = \frac{3}{4}$

STEP 5

Now that we have the remaining estate, we can find the fraction of the estate that goes to Charity A. This is $\frac{3}{5}$ of the remaining estate.
$state\, for\, Charity\, A = Remaining\, estate \\times Fraction\, for\, Charity\, A$

STEP 6

Plug in the values for the remaining estate and the fraction for Charity A to calculate the estate for Charity A.
$state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5}$

STEP 7

Calculate the estate for Charity A.
$state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5} = \frac{9}{20}$ The fraction of the estate that goes to Charity A is $\frac{9}{20}$ .

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The will divides the estate: $\frac{1}{4}$ to relatives, $\frac{3}{5}$ of the remaining to Charity A. What fraction of the estate goes to Charity A?

STEP 1

Assumptions1. The total estate is represented as1 (or100%) . $\frac{1}{4}$ of the estate is divided among relatives3. Of the remaining estate, $\frac{3}{5}$ goes to Charity A

STEP 2

First, we need to find the remaining estate after $\frac{1}{4}$ has been divided among relatives. We can do this by subtracting $\frac{1}{4}$ from1.
$Remaining\, estate = Total\, estate - Estate\, for\, relatives$

STEP 3

Now, plug in the given values for the total estate and the estate for relatives to calculate the remaining estate.
$Remaining\, estate =1 - \frac{1}{}$

STEP 4

Calculate the remaining estate.
$Remaining\, estate =1 - \frac{1}{4} = \frac{3}{4}$

STEP 5

Now that we have the remaining estate, we can find the fraction of the estate that goes to Charity A. This is $\frac{3}{5}$ of the remaining estate.
$state\, for\, Charity\, A = Remaining\, estate \\times Fraction\, for\, Charity\, A$

STEP 6

Plug in the values for the remaining estate and the fraction for Charity A to calculate the estate for Charity A.
$state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5}$

STEP 7

Calculate the estate for Charity A.
$state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5} = \frac{9}{20}$ The fraction of the estate that goes to Charity A is $\frac{9}{20}$ .

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The will divides the estate: 14\frac{1}{4}41​ to relatives, 35\frac{3}{5}53​ of the remaining to Charity A. What fraction of the estate goes to Charity A?

STEP 1

Assumptions1. The total estate is represented as1 (or100%) . 14\frac{1}{4}41​ of the estate is divided among relatives3. Of the remaining estate, 35\frac{3}{5}53​ goes to Charity A

STEP 2

STEP 3

Now, plug in the given values for the total estate and the estate for relatives to calculate the remaining estate.Remaining estate=1−1Remaining\, estate =1 - \frac{1}{}Remainingestate=1−1​

STEP 4

Calculate the remaining estate.Remaining estate=1−14=34Remaining\, estate =1 - \frac{1}{4} = \frac{3}{4}Remainingestate=1−41​=43​

STEP 5

STEP 6

Plug in the values for the remaining estate and the fraction for Charity A to calculate the estate for Charity A.state for Charity A=34times35state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5}stateforCharityA=43​times53​

STEP 7

Calculate the estate for Charity A.state for Charity A=34times35=920state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5} = \frac{9}{20}stateforCharityA=43​times53​=209​The fraction of the estate that goes to Charity A is 920\frac{9}{20}209​.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

The will divides the estate: $\frac{1}{4}$ to relatives, $\frac{3}{5}$ of the remaining to Charity A. What fraction of the estate goes to Charity A?

Assumptions1. The total estate is represented as1 (or100%) . $\frac{1}{4}$ of the estate is divided among relatives3. Of the remaining estate, $\frac{3}{5}$ goes to Charity A

Now, plug in the given values for the total estate and the estate for relatives to calculate the remaining estate.
$Remaining\, estate =1 - \frac{1}{}$

Calculate the remaining estate.
$Remaining\, estate =1 - \frac{1}{4} = \frac{3}{4}$

Plug in the values for the remaining estate and the fraction for Charity A to calculate the estate for Charity A.
$state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5}$

Calculate the estate for Charity A.
$state\, for\, Charity\, A = \frac{3}{4} \\times \frac{3}{5} = \frac{9}{20}$ The fraction of the estate that goes to Charity A is $\frac{9}{20}$ .