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QuestionA will divides 12\frac{1}{2} of the estate among relatives. 15\frac{1}{5} of the remaining goes to charity A. Find the fraction for charity A.

Studdy Solution

STEP 1

Assumptions1. The total estate is considered as1 or100%. . Half of the estate is divided among relatives.
3. Of the remaining estate, a fifth goes to charity A.

STEP 2

First, we need to find the fraction of the estate that remains after half is divided among relatives. We can do this by subtracting the fraction given to relatives from the total estate.
Remaining estate=Total estate−Estate given to relativesRemaining\, estate = Total\, estate - Estate\, given\, to\, relatives

STEP 3

Now, plug in the given values for the total estate and the estate given to relatives to calculate the remaining estate.
Remaining estate=1−12Remaining\, estate =1 - \frac{1}{2}

STEP 4

Calculate the remaining estate.
Remaining estate=1−12=12Remaining\, estate =1 - \frac{1}{2} = \frac{1}{2}

STEP 5

Now that we have the remaining estate, we can find the fraction that goes to charity A. This is a fifth of the remaining estate.
state to charity A=Remaining estatetimesFraction given to charity Astate\, to\, charity\, A = Remaining\, estate \\times Fraction\, given\, to\, charity\, A

STEP 6

Plug in the values for the remaining estate and the fraction given to charity A to calculate the estate to charity A.
state to charity A=12times15state\, to\, charity\, A = \frac{1}{2} \\times \frac{1}{5}

STEP 7

Calculate the estate to charity A.
state to charity A=12times15=110state\, to\, charity\, A = \frac{1}{2} \\times \frac{1}{5} = \frac{1}{10}The fraction of the estate that goes to charity A is 110\frac{1}{10}.

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