Let's solve the problem step by step:
Let the two numbers be represented by 'x' and 'y'.
Given information:
- When the sum of two numbers is divided by 3, the quotient is 4 and the remainder is 1: (x + y) ÷ 3 = 4 with remainder 1.
- When the difference of the two numbers is divided by 2, the quotient is 2 and the remainder is 1: (x - y) ÷ 2 = 2 with remainder 1.
We can solve this problem using a system of equations.
From the first given information: (x + y) ÷ 3 = 4 with remainder 1
We can write this equation as: (x + y) = 4(3) + 1 x + y = 12 + 1 x + y = 13
From the second given information: (x - y) ÷ 2 = 2 with remainder 1
We can write this equation as: (x - y) = 2(2) + 1 x - y = 4 + 1 x - y = 5
Now we have a system of equations: Equation 1: x + y = 13 Equation 2: x - y = 5
We can solve this system of equations by either substitution or elimination method.
Using the elimination method: Add Equation 1 and Equation 2: (x + y) + (x - y) = 13 + 5 2x = 18 x = 18 ÷ 2 x = 9
Substitute x = 9 into Equation 1 to find the value of y: 9 + y = 13 y = 13 - 9 y = 4
Therefore, the numbers are 9 and 4.
