The sum of two numbers is 143. If the greater number is divided by the difference of the numbers, the quotient is 7. What is the difference of the two numbers ?<\/p>\n
[amp_mcq option1=”9″ option2=”11″ option3=”14″ option4=”15″ correct=”option2″]<\/p>\n
From the second equation, we get:
\n\\(x = 7(x – y)\\)
\n\\(x = 7x – 7y\\)
\n\\(7y = 7x – x\\)
\n\\(7y = 6x\\)
\n\\(x = \\frac{7y}{6}\\)<\/p>\n
Now substitute this expression for \\(x\\) into the first equation:
\n\\(\\frac{7y}{6} + y = 143\\)
\nTo combine the terms on the left side, find a common denominator:
\n\\(\\frac{7y + 6y}{6} = 143\\)
\n\\(\\frac{13y}{6} = 143\\)
\n\\(13y = 143 \\times 6\\)
\n\\(y = \\frac{143 \\times 6}{13}\\)
\nSince \\(143 = 13 \\times 11\\), we have:
\n\\(y = \\frac{13 \\times 11 \\times 6}{13}\\)
\n\\(y = 11 \\times 6\\)
\n\\(y = 66\\)<\/p>\n
Now find the value of \\(x\\) using \\(x = \\frac{7y}{6}\\):
\n\\(x = \\frac{7 \\times 66}{6}\\)
\n\\(x = 7 \\times 11\\)
\n\\(x = 77\\)<\/p>\n