Question

A school has 345 teachers and pupils. There are 4 times as many boys as teachers and there are 12 more girls than boys. How many pupils are there?

Answer 1

$\sf\large\underline{Let:}$

• $\rm{The\: Number\:of\: teachers=x}$
• $\rm{The\: Number\:of\: boys=4x}$
• $\rm{The\: Number\:of\: girls=4x+12}$

$\sf\large\underline{To\: Find:}$

• $\rm{The\: Number\:of\:pupils=?}$

$\sf\large\underline{Given:}$

• A school has 345 teachers and pupils. There are
• 4 times as many boys as teachers and there are 12 more girls than boys.]

$\sf\large\underline{A.T.Q:}$

$\rm{\implies Sum\:of\:boys+girls+teachers=Total}$

$\rm{\implies 4x+4x+12+x=345}$

$\rm{\implies 9x+12=345}$

$\rm{\implies 9x=345-12}$

$\rm{\implies 9x=333}$

$\rm{\implies x=37}$

• Now, calculate the number of boys and girls and teachers here]

$\rm{\implies Number\:_{boys}=4x}$

$\rm{\implies Number\:_{boys}=4\times\:37}$

$\rm{\implies Number\:_{boys}=148}$

$\rm{\implies Number\:_{girls}=4x+12}$

$\rm{\implies Number\:_{girls}=4\times\:37+12}$

$\rm{\implies Number\:_{girls}=148+12}$

$\rm{\implies Number\:_{girls}=160}$

$\rm{\implies Number\:_{teachers}=x}$

$\rm{\implies Number\:_{teachers}=37}$

• Now , calculate total number of pupils here]

$\rm{\implies No\:of\:boys+No\:of\: girls}$

$\rm{\implies 148+160}$

$\rm{\implies 308}$

$\sf\large{Hence,}$

$\rm{\implies Total\:_{Pupils\:in\: school}=308}$

Answer 2

number of teachers = x .....(1)

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number of boys = 4x ....(2)

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number of girls = 4x + 12 ......(3)

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

solution : -

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

sum of eq 1 , 2 , 3

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teacher + boy + girl = 345

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

x + 4x + 4x + 12 = 345

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

9x = 345 - 12

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x = 37

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so,

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no. of boys = 4x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀= 4 x 37

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀= 148

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

no. of girls = 4x + 12

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀= 4 x 37 + 12

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀= 148 + 12

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀= 160

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

pupils = 148 + 160

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀= 308