Question

The number is between 8,500 and 8,800.

When multiplied by 8, the result is a whole number.
The digit in the hundreds place is ¾ the digit in the thousands place.
The sum of all digits in the number is 26.
The digit in the hundredths place is 200% of the digit in the tenths place.
There are no zeros in the decimal places.

Your first job is to post at least two numbers that do NOT work.
Explain why they do not work.
Post your best guess for a number that works (or a number that almost works)

Answer 1

The number is 8,639. Why? Well, see below!

We can use variables ABCD to Stand in place of the numbers.

A + B + C + D = 26

Since the number is between 8,500 and 8,800, A is 8.

The digit in the hundreds place is 3/4 of the thousands place, so:

8 x 3/4 = 24/4
24/4 reduces to 6
B = 6

The digit in the hundreds place is 200% of the digit in the tens place, so:

6 / 2 = 3
C = 3

The last step is simple! Since we have our values, we can use inverse operations to solve.

8 + 6 + 3 + D = 26
17 + D = 26
26 - 17 = 9
D = 9

Hence, your number is 8,639.


Two numbers that will not work:

7 in the thousands place would not work. It would not work because the problem says that the number is between 8,500 and 8,800, and would therefore mean the number can be 8,500 at least.

Another number that would not work would be 2 in the hundreds place. This number would not work because a 1 would be in the tens place, and 3 + 8 = 11. This seems right, but it isn’t because 11 + 15 = 26. That would mean that in order to add up, the digits would have to expand higher than 8 in the thousands place and we would possibly need to use the ten thousands place.

If you need help, let me know and I will gladly assist you.