Question

the sum of three numbers is 75.the second number is 3 less than the first number and the third number is four times the first . What are the three numbers?

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{The\:3\: Number's\:are}$
• $\rm{1st\: Number=x}$
• $\rm{2nd\: Number=x-3}$
• $\rm{3rd\: Number=4x}$

$\rm{Given,\:The\:sum\:of\:3\: Number's=75}$

$\small{\underline{\purple{\rm{As\:per\:the\: Question:}}}}$

$\rm{\implies x+x-3+4x=75}$

$\rm{\implies 6x-3=75}$

$\rm{\implies 6x=75+3}$

$\rm{\implies \cancel{6}x=\cancel{78}}$

$\rm\red{\implies x=13}$

Hence,

$\rm\green{\implies 1ST\:_{Number}=x=13}$

$\rm\purple{\implies 2ND\:_{Number}=x-3=13-3=10}$

$\rm\red{\implies 3RD\:_{Number}=4x=4*13=52}$

$\large{\underline{\orange{\rm{Verification:}}}}$

$\rm{\implies x+x-3+4x=75}$

• $\rm{putting\:the\:value\:x=13}$

$\rm{\implies 13+13-3+4*13=75}$

$\rm{\implies 13+13-3+52=75}$

$\rm{\implies 78-3=75}$

$\rm\green{\implies 75=75}$

$\large{\underline{\orange{\rm{Hence,\: Verified:}}}}$

Answer 2

Step-by-step explanation:

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