Ineed with my homework answer this correctly

Find 41 on the number line. This is the total of the two numbers you're looking for.

When you cut it in half, you have 2 numbers that add to 41, the one on the left (20.5) and the difference between it and 41 (also 20.5). If you move your cut point half a unit to the left, now you have the numbers 20 and 21. They differ by 1 unit. Their difference is twice the number of units you have moved the cut point.

For a difference of 25, you will need to move the cut point 25/2 = 12.5 units to the left of 20.5, to 8. So, one of your numbers is 8 and the other is the difference from that and 41, which is 33.

Your numbers are 8 and 33.

Remark

I don't think you are intended to use algebra. If you are, leave a note and one of us will get back to you.

I think the best way to tackle this problem is to start with the sum. And then look at the difference.

Solve

What does the sum tell you? It tells you that there are two whole numbers that add to 41. Let's take two extremes.

Solution 1

Take two numbers that are close together. 20 and 21 are very close together. They add to 41. Their difference is 1

Now take 2 numbers that are far apart like 40 and 1. That gives a difference of 39. Which result is closes to the difference of 25? The bottom one  is a little closer to a difference of 25. So work from that. Make a table

Largest Number        Second Number         Sum           Difference

      39                               2                               41                 37

      37                                4                               41                33

      35                                6                               41                29

      34                                7                               41                27  

      33                                8                               41                25

The two numbers that resolve the problem are 33 and 8 which has a difference of 25.

The last line is your answer. 33 and 8 <<<< Answer  

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