17 the larger of two number is divided by the smaller,the quotient and the reminder are 2 each. 17 5times the smaller number is divided by the larger,the quotient and the reminder are still 2 each. Find the two number.

What does 17 have to do with this problem?

To solve this problem, let's assign variables to the two numbers. Let's say the larger number is L and the smaller number is S.

According to the problem, when the larger number is divided by the smaller number, the quotient (result) is 2, and the remainder is also 2. This can be written as:

L = 2S + 2 ----- (Equation 1)

Now, we are also given that when 17 (5 times the smaller number) is divided by the larger number, the quotient is 2, and the remainder is 2. This can be written as:

17 = 2L + 2S ----- (Equation 2)

Now we have two equations: Equation 1 and Equation 2. To solve the system of equations, we can substitute Equation 1 into Equation 2:

17 = 2(2S + 2) + 2S
17 = 4S + 4 + 2S
17 = 6S + 4
17 - 4 = 6S
13 = 6S
S = 13/6

Now we substitute the value of S back into Equation 1 to find the value of L:

L = 2(13/6) + 2
L = 26/6 + 2
L = 26/6 + 12/6
L = 38/6
L = 19/3

Therefore, the smaller number (S) is 13/6 and the larger number (L) is 19/3.