The sum of two numbers is 143. If the greater number is divided by the

From the second equation, we get:
\(x = 7(x – y)\)
\(x = 7x – 7y\)
\(7y = 7x – x\)
\(7y = 6x\)
\(x = \frac{7y}{6}\)

Now substitute this expression for \(x\) into the first equation:
\(\frac{7y}{6} + y = 143\)
To combine the terms on the left side, find a common denominator:
\(\frac{7y + 6y}{6} = 143\)
\(\frac{13y}{6} = 143\)
\(13y = 143 \times 6\)
\(y = \frac{143 \times 6}{13}\)
Since \(143 = 13 \times 11\), we have:
\(y = \frac{13 \times 11 \times 6}{13}\)
\(y = 11 \times 6\)
\(y = 66\)

Now find the value of \(x\) using \(x = \frac{7y}{6}\):
\(x = \frac{7 \times 66}{6}\)
\(x = 7 \times 11\)
\(x = 77\)

The two numbers are 77 and 66.
The question asks for the difference of the two numbers, which is \(x – y\):
Difference = \(77 – 66 = 11\)