if Mark sells 7 cars to John, John will have as many cars as Mark
On the other hand, if John sells 7 cars to Mark, Mark will have twice as many cars as John.
How many cars do each manager have without any cars changing ownership?
Hi Dr Peterson, thank you for your reply. I tried to use Algebra but was getting nowhere so I wrote down the multiple of 7 and figured out that the answer was 35/49 but would like to use Algebra to logically explain this to my daughter.
Okay, so you used a reasonable trial-and-error, or search, method to find an answer. There are other ways without algebra, but there's no need to look further.
First, let's check it to see if your answer is right.
I assume you are saying that John has 35 and Mark has 49.
If Mark sells 7 to John, then John will have 35+7 = 42, and Mark will have 49-7 = 42. So that's good.
If John sells 7 to Mark, then Mark will have 49+7 = 56, and John will have 35-7 = 28. Since 56 is twice 28, that's good too.
Now to use algebra, we just use letters in place of those numbers. Here is a cut and paste from what I just said:
Suppose that John has J and Mark has M.
If Mark sells 7 to John, then John will have J+7, and Mark will have M-7. We want these to be equal: J+7 = M-7.
If John sells 7 to Mark, then Mark will have M+7, and John will have J-7. We want the first to be twice the second: M+7 = 2(J-7).
Now you have two equations in two unknowns, and you can solve for J and M.
Do you see how either trial and error, or a practice check, can be a model for writing equations? That's a good thing to know.
Now, because you didn't show any of your thinking using algebra, I don't know whether you can handle two equations. Please give it a try, and if you still have trouble, show me some work so I can help you with your actual difficulties.
