Write one digit on each side of 92 to make a four digit multiple of 45. How many different solutions does this problem have?

Two solutions:

Adding 7 to the left and 0 to the right: 7920

Adding 2 to the left and 5 to the right: 2925

Step-by-step explanation:

The multiples of 45 always have as last digit 0 or 5, so the digit to the right of 92 has to be 0 or 5.

If we use 0 as the last digit, our options of multiples will be just 7920 (7920 = 45 * 176)

If we use 5 as the last digit, our option of multiples will be just 2925 (2925 = 45 * 65)

So we have just two solutions for this problem:

Adding 7 to the left and 0 to the right: 7920

Adding 2 to the left and 5 to the right: 2925