Question

The difference between two numbers is 26 and one number is three times the other. Find the numbers.​

Answer 1

$\huge\sf\red{\underline{\underline{Given}}}\::$

$\begin{cases}\sf\gray{The\: difference\: between \:the\: two \:numbers\: is \:26.} \\ \sf\gray{One\: number\: is \:three \:times \:the\: other.}\end{cases}$

$\huge\sf\blue{\underline{\underline{To\:Find}}}\::$

$\begin{cases}\sf\gray{The\: required\: numbers}\end{cases}$

$\huge\sf\pink{\underline{\underline{Solution}}}\::$

$\bf Let \begin{cases}\sf\gray{Larger\: number \:be\: x}\\ \sf\gray{Smaller\: number\: be \:y}\end{cases}$

$\sf\underline{\orange{Now, According\:to\:1^{st} \: condition}}$

$\mapsto\:\: \sf\green {x - y = 26 ................(1)}$

$\sf\underline{\orange{According\:to\:2^{nd} \: condition}}$

$\mapsto \sf\green {x = 3y............... (2) }$

$\sf\underline{\orange{Putting\:eq\:(2)\: in \:(1)\::}}$

$\longmapsto\:\:\: \sf \purple{x - y = 26}$

$\longmapsto \:\:\:\sf \green{(3y) - y = 26}$

$\longmapsto\:\:\: \sf \purple{2y = 26}$

$\longmapsto\:\:\: \sf \green{y = \dfrac{\cancel{26}}{\cancel{2}} }$

$\longmapsto\:\:\: \sf \underline\pink{y = 13}$

$\sf\underline{\orange{Now,\: substitute\:y\: value\:in\:eq\:(2)}}$

$\hookrightarrow\:\:\: \sf\purple {x = 3y}$

$\hookrightarrow\:\:\: \sf\green {x = 3 \times 13 }$

$\hookrightarrow\:\:\: \sf\underline\pink {x\: =\: 39}$

$\star\:\sf\underline\red{Hence,\:The\: required\: numbers\:are\:39\:\:\&\:\:13}$