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QuestionA town has a population of 90009000, with 39\frac{3}{9} males. If 40%40\% of males are married, find the % of married females. (a) 50%50\% (b) 40%40\% (c) 45%45\% (d) None of these

Studdy Solution

STEP 1

Assumptions1. The total population of the town is9000. . 39\frac{3}{9} of the population are males.
3. The rest of the population are females.
4. 40%40\% of the males are married.

STEP 2

First, we need to find the number of males in the town. We can do this by multiplying the total population by the fraction of males.
Males=Total populationtimesFraction of malesMales = Total\, population \\times Fraction\, of\, males

STEP 3

Now, plug in the given values for the total population and the fraction of males to calculate the number of males.
Males=9000times39Males =9000 \\times \frac{3}{9}

STEP 4

Calculate the number of males.
Males=9000times39=3000Males =9000 \\times \frac{3}{9} =3000

STEP 5

Now that we have the number of males, we can find the number of females by subtracting the number of males from the total population.
emales=Total population−Malesemales = Total\, population - Males

STEP 6

Plug in the values for the total population and the number of males to calculate the number of females.
emales=9000−3000emales =9000 -3000

STEP 7

Calculate the number of females.
emales=9000−3000=6000emales =9000 -3000 =6000

STEP 8

Now, we need to find the number of married males. We can do this by multiplying the number of males by the percentage of married males.
Married males=MalestimesPercentage of married malesMarried\, males = Males \\times Percentage\, of\, married\, males

STEP 9

Now, plug in the given values for the number of males and the percentage of married males to calculate the number of married males.
Married males=300times40%Married\, males =300 \\times40\%

STEP 10

Convert the percentage to a decimal value.
40%=0.440\% =0.4Married males=3000times0.4Married\, males =3000 \\times0.4

STEP 11

Calculate the number of married males.
Married males=3000times0.4=1200Married\, males =3000 \\times0.4 =1200

STEP 12

Now that we have the number of married males, we can find the number of married females by subtracting the number of married males from the total number of married people (which is equal to the number of males since all males are married).
Married females=Males−Married malesMarried\, females = Males - Married\, males

STEP 13

Plug in the values for the number of males and the number of married males to calculate the number of married females.
Married females=3000−1200Married\, females =3000 -1200

STEP 14

Calculate the number of married females.
Married females=3000−1200=1800Married\, females =3000 -1200 =1800

STEP 15

Now that we have the number of married females, we can find the percentage of married females by dividing the number of married females by the total number of females and multiplying by100.
Percentage of married females=Married femalesemalestimes100Percentage\, of\, married\, females = \frac{Married\, females}{emales} \\times100

STEP 16

Plug in the values for the number of married females and the total number of females to calculate the percentage of married females.
Percentage of married females=18006000times100Percentage\, of\, married\, females = \frac{1800}{6000} \\times100

STEP 17

Calculate the percentage of married females.
Percentage of married females=18006000times100=30%Percentage\, of\, married\, females = \frac{1800}{6000} \\times100 =30\%The percentage of married females is30%.

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