## MauriceLong 2 years ago I need help with this problem please? and thank you. In a recent year, the total sales at Restaurant A were \$350,000 more than Restaurant B. Total Sales at the two stores were \$600,000,000. What were the sales for the year at each store? What was the amount of sales for the year at Restaurant B What was the amount of sales for the year at at Restaurant A

1. Schrodinger

Okay, let's set it up like an equation. So, you have Restaurant A and B, each can be described as: \[A = B + 350,000\]And\[A + B = 600,000,000.\]Do we agree on this?

2. MauriceLong

yes

3. Emah

I think all you would need to do is, subtract the 350,000 from 600,00,000, then divide by 2... yeah i agree with @Schrodinger

4. Schrodinger

Okay. Since you're dealing with a system of equations, what would be the next step? In this situation, it should be clear that you can substitute.

5. MauriceLong

How would you subsitute

6. Schrodinger

In order to substitute, you'd just find the same variable in both equations, isolate the variable that you want to substitute something in for, and then put it in place of the variable in the other equation. Let's break this down: Between the first and second equation, both have A and B, while the first one has A on the left side alone, and B + 350,000 on the right, yes? Because A is alone on the left side, that means it's already isolated. That means you can put the right side of the first equation (B + 350,000) in place of A in the second equation, because that equals A. So, let's take the second equation and substitute A for \[B + 350,000\]So the only variable you have is B.

7. MauriceLong

Ok

8. Schrodinger

Putting that in, we get:\[(B + 350,000) + B = 600,000,000\]From there, we can add like terms.\[2B + 350,000 = 600,000,000\]Next, you would isolate B by subtracting 350,000 from both sides. \[2B = 599,650,000\]Then you can divide to find B! After that, all you need to do is plug that value in to either equation to find A.

9. MauriceLong

ok so B =599,650,00

10. Schrodinger

Sorry, nope. Take a closer look, that's\[2B = 599,650,000\]Right? What would you need to do to get B itself?

11. MauriceLong

I think I would need too subtract

12. Schrodinger

But there's nothing left to subtract. Okay, let me give you an example. Let's say you have \[5x = 10\]What would be the next step you could take to find x?

13. MauriceLong

divide

14. Schrodinger

Yeah! You would divide by two, exactly! So let's look at the actual problem. \[2B = 599,650,000\]B is being multiplied by something here. What would you have to do in order to get just plain old B?