## Find the values of x, y and z

xy and yx are 2-digit numbers, which together add up to the 3-digit number zxz.

xy + yx = zxz

The largest number that can be formed by adding two 2-digit numbers is:

99+99 = 198

Now if the number zxz is 3 digits, and the largest number it can be is 198, then we conclude that **z = 1**.

If z = 1 the sum result is 1x1.

The values of x and y that satisfy the equation xy + yx = 1x1 are as follows:

x = 2 and y = 9, ie 29 + 92 = 121

Answer: x = 2, y = 9, z = 1

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