what can i multiply with any digit to get the answer 8

Question

Eva wants to have the answer to always be 8. she thinks changing the line "multiply the sum by 2" to "multiply the sum  by 4" will make that hapen. her friend john is a math genius and tells her she'd have to change that line and one other line so that the answer is always 8. what line also needs to be change to what so that the answer is always 8. explain how you know.

Answer 1

Eva is given the following steps:

1) Add two numbers.

2) Multiply the sum by 2.

3) The answer is 8.

She thinks the steps should be:

1) Add two numbers.

2) Multiply the sum by 4.

3) The answer is 8.

We add an extra step:

1) Add two numbers.

Extra step 1a) Adjust the sum to 2 by adding or subtracting.

2) Multiply the sum/difference by 4.

3) The answer is 8.

So the extra step is to work out the actual sum of the two numbers then reduce or increase it to get 2.

Let's suppose the two numbers are 6 and -2, so their sum is actually 4. The extra step would be to subtract 2:

1) Add 6 and -2.

1a) Subtract 2.

2) Multiply by 4.

3) The answer is 8.

The original question could have been:

1) Add 6 and -2.

2) Multiply by 2.

3) The answer is 8.