Question
The difference between two numbers is 7. Six times the smaller plus the larger is 77. Find the numbers.
✓
Answer
Let the smallest number $=x$
and the largest number $=\mathrm{y}$
According to the condition,
$ y-x=7 $...(i)
$ \text { and } 6 x+y=77 $....(ii)
From eq. (i)
$ y=7+x $...(ii)
Substitute the eq. (iii) in eq. (ii)
$ \begin{aligned} & 6 x+7+x=77 \\ & \Rightarrow 7 x=77-7 \\ & \Rightarrow x=\frac{70}{7}=10 \end{aligned} $
Now, substitute the value of $x$ in eq. (iii)
$ y=7+10=17 $
$\therefore$ The smallest number 10 and the largest number is 17 .
and the largest number $=\mathrm{y}$
According to the condition,
$ y-x=7 $...(i)
$ \text { and } 6 x+y=77 $....(ii)
From eq. (i)
$ y=7+x $...(ii)
Substitute the eq. (iii) in eq. (ii)
$ \begin{aligned} & 6 x+7+x=77 \\ & \Rightarrow 7 x=77-7 \\ & \Rightarrow x=\frac{70}{7}=10 \end{aligned} $
Now, substitute the value of $x$ in eq. (iii)
$ y=7+10=17 $
$\therefore$ The smallest number 10 and the largest number is 17 .
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