Question

The ratio of males to females at a party is 3 : 5

There are 12 more females than males.

How many people are at the party?

Answer 1

Answer:

Step-by-step explanation:

5x-3x=12

2x=12

x=6

no.of male=3x6=18

no.of female=5x6=30

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Answer 2

Correct Question-:

• The ratio of males to females at a party is 3 : 5 . There are 12 more females than males. How many people are at the party ?

AnswEr-:

• $\red{\underline{\boxed{\sf{Total\:Number\:of\:people\:=\:48\:People.}}}}$

Explanation-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\:ratio\:of\:males \:to \:females \:in\:the \:party\:is\:= \frak{3:5}} & \\\\ \sf{ There\: are\: 12 \:more\: females\: than\: males\:. }\end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{The\:total\:numbers \:of\:people \;in\:party\:.\: }\end{cases}$

$\dag {\underline {\sf{\large { Solution \:of\:Question\:-: }}}}$

• $\frak{Let's \:Assume \: -:} \begin{cases} \sf{The\:\:numbers \:of\:male\:and\:females \;in\:party\:be \:3x \:and\:5x.\: }\end{cases}$

$\star {\bigstar {\sf{\large { Then -: }}}}$

• $\frak{Number \:of\:males\:and\:females \:\: -:} \begin{cases} \sf{The\:numbers\:of\:males \: \: \:in\:the \:party\:is\:= \frak{3x}} & \\\\ \sf{ The\:numbers\:of\:females \: \: \:in\:the \:party\:is\:= \frak{5x} }\end{cases}$

$\star {\underline {\sf{\large { Given \:that-: }}}}$

• $\sf{There\: are\: 12 \:more\: females\: than\: males\:.}$

• $\sf{Then,}$

• $\sf{Equation \:Formed\:=\:5x-3x=12\:.}$

$\star {\bigstar {\sf{\large { Now , \:Solving\:for\:x\:in\:Equation\:-: }}}}$

• $\implies{\sf{Equation \: \:=\:5x-3x=12\:.}}$

• $\implies{\sf{\:5x-3x=12\:.}}$

• $\implies{\sf{\:2x=12\:.}}$

• $\implies{\sf{\:x=\dfrac{12}{2}\:.}}$

• $\implies{\sf{\:x=6\:.}}$

$\star {\bigstar {\sf{\large { Therefore -: }}}}$

• $\star {\underline {\sf{\large { The\:Value \:of\:x\:is\:6 }}}}$

$\star {\bigstar {\sf{\large { Then -: }}}}$

• $\frak{Putting \:x\:=6 \:\: -:} \begin{cases} \sf{The\:numbers\:of\:males \: \: \:in\:the \:party\:is\:= \frak{3x=3\times 6 = 18\: males}} & \\\\ \sf{ The\:numbers\:of\:females \: \: \:in\:the \:party\:is\:= \frak{5x=5\times 6 = 30 \:females } }\end{cases}$

$\star {\bigstar {\sf{\large { Therefore-: }}}}$

• $\sf{There\: are\: 18 \:\: males\:and\:30\:females \:in\:the\:party.\:.}$

$\star {\bigstar {\sf{\large { Then -: }}}}$

• $\red{\underline{\boxed{\sf{Total\:Number\:of\:people\:=\:Number\:of\:males \:+ Number\:of\:Females.}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{The\:numbers\:of\:males \: \: \:in\:the \:party\:is\:= \frak{ 18\: males}} & \\\\ \sf{ The\:numbers\:of\:females \: \: \:in\:the \:party\:is\:= \frak{ 30 \:females } }\end{cases}$

$\star {\bigstar {\sf{\large { Then -: }}}}$

• $\implies{\sf{\:18 +30\:.}}$

• $\implies{\sf{\:48 \: peoples\:.}}$

$\star {\bigstar {\sf{\large { Hence-: }}}}$

• $\red{\underline{\boxed{\sf{Total\:Number\:of\:people\:=\:48\:People.}}}}$

_____________________________

$\star {\bigstar {\sf{\huge { ♡ Verification-: }}}}$

$\star {\underline {\sf{\large { Given \:that-: }}}}$

• $\sf{There\: are\: 12 \:more\: females\: than\: males\:.}$

• $\sf{Then,}$

• $\sf{Equation \:Formed \:=\:5x-3x=12\:.}$

$\star {\underline {\sf{\large { Here-: }}}}$

• $\implies{\sf{\:x=6\:.}}$

$\star {\bigstar {\sf{\large { Now , \:Putting \:x=6\:in\:Equation\:-: }}}}$

• $\implies{\sf{Equation \:Formed \:=\:5x-3x=12\:.}}$
• $\implies{\sf{\:5\times 6 -3 \times 6 =12\:.}}$

• $\implies{\sf{\:30 -18=12\:.}}$

• $\implies{\sf{\:12 =12\:.}}$

Therefore,

• $\star {\bigstar {\sf{\large { LHS = RHS }}}}$

• $\star {\bigstar {\sf{\large { Hence, \:Verified}}}}$

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