Question

The sum of two numbers is eighty-three. If the larger number is divided by the smaller number, then both the quotient and the remainder are six. Find the numbers .

Answer 1

• The numbers are 72 and 11

Explanation:

Let the number be x and y.

Given

• x + y = 83,
• x = 6y + 6

Solve the system by substitution:

• 6y + 6 + y = 83
• 7y = 83 - 6
• 7y = 77
• y = 11

Find x:

• x + 11 = 83
• x = 83 - 11
• x = 72