In a village, the number of female is greater than the number of males

1.	In a village, the number of female is greater than the number of males by 31500. If the ratio of the number of females and males is 8:5, find the number of females and males
Answer» $\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{Number_{(females)} - Number_{(males)} = 31500} \\ &\sf{Number_{(females)}:Number_{(males)} = 8:5 } \end{cases}\end{gathered}\end{gathered}$ $\begin{gathered}\begin{gathered}\bf \:To\:find - \begin{cases} &\sf{Number_{(females)} \: and \: Number_{(males)}} \end{cases}\end{gathered}\end{gathered}$ Basic Concept Used :- Writing SYSTEMS of Linear Equations from Word Problem. Step :- 1 Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find. Step :- 2 TRANSLATE the problem to an equation. Assign a VARIABLE (or variables) to represent the unknown. Clearly state what the variable represents. Step :- 3 Carry out the plan and SOLVE the problem. $\large\underline{\bold{Solution-}}$ Given that Number of females to the number of males are in the ratio 8 : 5. So, $\begin{gathered}\begin{gathered}\bf \: Let \: \begin{cases} &\sf{Number_{(females)} \: = \: 8x} \\ &\sf{Number_{(males)} \: = \: 5x} \end{cases}\end{gathered}\end{gathered}$ Further, It is given that The number of female is greater than the number of males by 31500. $\rm :\longmapsto\:Number_{(females)} - Number_{(males)} = 31500$ $\rm :\longmapsto\:8x - 5x = 31500$ $\rm :\longmapsto\:3x = 31500$ $\bf\implies \:x = 10500$ $\begin{gathered}\begin{gathered}\bf \: Hence - \: \begin{cases} &\sf{Number_{(females)} \: = \: 8x = 84000} \\ &\sf{Number_{(males)} \: = \: 5x = 52500} \end{cases}\end{gathered}\end{gathered}$

In a village, the number of female is greater than the number of males by 31500. If the ratio of the number of females and males is 8:5, find the number of females and males

Answer»

$\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{Number_{(females)} - Number_{(males)} = 31500} \\ &\sf{Number_{(females)}:Number_{(males)} = 8:5 } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\:find - \begin{cases} &\sf{Number_{(females)} \: and \: Number_{(males)}} \end{cases}\end{gathered}\end{gathered}$

Basic Concept Used :-

Writing SYSTEMS of Linear Equations from Word Problem.

Step :- 1 Understand the problem.

Understand all the words used in stating the problem.

Understand what you are asked to find.

Step :- 2 TRANSLATE the problem to an equation.

Assign a VARIABLE (or variables) to represent the unknown.

Clearly state what the variable represents.

Step :- 3 Carry out the plan and SOLVE the problem.

$\large\underline{\bold{Solution-}}$

Given that

Number of females to the number of males are in the ratio 8 : 5.

So,

$\begin{gathered}\begin{gathered}\bf \: Let \: \begin{cases} &\sf{Number_{(females)} \: = \: 8x} \\ &\sf{Number_{(males)} \: = \: 5x} \end{cases}\end{gathered}\end{gathered}$

Further,

It is given that

The number of female is greater than the number of males by 31500.

$\rm :\longmapsto\:Number_{(females)} - Number_{(males)} = 31500$

$\rm :\longmapsto\:8x - 5x = 31500$

$\rm :\longmapsto\:3x = 31500$

$\bf\implies \:x = 10500$

$\begin{gathered}\begin{gathered}\bf \: Hence - \: \begin{cases} &\sf{Number_{(females)} \: = \: 8x = 84000} \\ &\sf{Number_{(males)} \: = \: 5x = 52500} \end{cases}\end{gathered}\end{gathered}$

In a village, the number of female is greater than the number of males by 31500. If the ratio of the number of females and males is 8:5, find the number of females and males

Basic Concept Used :-

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