Question

Two numbers add up to 70. One third of the larger number is 10 more than one
seventh of the smaller number. Find the numbers.
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Answer 1

Answer:

Larger number = 42 and smaller number = 28

Let the larger number be x.

and smaller numaber be y.

according to question

\begin{gathered}x+y=70-(i)\\\therefore\frac{1}{3}of x=\frac{1}{7}of y+10\\\frac{x}{3}=\frac{y}{7}+10\\\frac{x}{3}-\frac{y}{7}=10-(ii)\end{gathered}x+y=70−(i)∴31ofx=71ofy+103x=7y+103x−7y=10−(ii)

Solving equation (i) and (ii)

Multiply \frac{1}{7}71 in equation(i) and 1 in equation (i)

\begin{gathered}x+y=70- (i)\times\frac{1}{7}\\\frac{x}{3}-\frac{y}{3}=10-(ii)\times1\\\end{gathered}x+y=70−(i)×713x−3y=10−(ii)×1

\begin{gathered}\frac{x}{7}+\frac{y}{7}=\frac{70}{7}\\\frac{x}{3}-\frac{y}{7}=10\\\frac{x}{7}+\frac{y}{7}=10-(iv)\\\frac{x}{3}-\frac{y}{7}=10-(v)\end{gathered}7x+7y=7703x−7y=107x+7y=10−(iv)3x−7y=10−(v)

Adding equation (iv) and (v)

\begin{gathered}\frac{x}{7}+\frac{y}{7}+(\frac{x}{3}-\frac{y}{3})=10+10\\\frac{x}{7}+\frac{x}{3}=20\\\\\frac{10x}{21}=20\\x=42\end{gathered}7x+7y+(3x−3y)=10+107x+3x=202110x=20x=42

put x=42x=42 in equation (i)

\begin{gathered}42+y=70\\y=28\end{gathered}42+y=70y=28