Write one digit on each side of 23 to make a four digit multiple of 72. How many different solutions does this problem have?

This problem has two possible solutions.

2232

7236

Step-by-step explanation:

To be divisible by 72, a number has:

To be divisible by both 8 and 9 at the same time.

It is divisible by 8 if it's last two digits are divisible by 4.

It is divisible by 9 it the sum of it's digits is a number divisible by 9.

a23b

3b must be divisible by 4. In the thirties, the numbers that are divisible by 4 are 32 and 36. So b = 2 or b = 6.

a232

2 + 3 + 2 = 7

The higest possible value of a is 9 and the lowest is 1.

Between 8 and 16, only 9 is divisible by 9. So a = 2.

a = 2, b = 2 is one of the solutions.

a236

2 + 3 + 6 = 11

The higest possible value of a is 9 and the lowest is 1.

Between 12 and 20, only 18 is divisible by 9. So we need a = 7

the answer is 37

step-by-step explanation:

location: point 0

step-by-step explanation:

well, -8 to 10 on a number line is 18 spaces.

1/9 of 18 is 2.

so, 4/9 of 18 must be 8.

8 spaces from -8 (a) is 0.

so, 4/9 of the way from -8 to 10 is 0!