A local hamburger shop sold a combined total of 600 hamburgers and cheeseburgers on Friday. There were 50 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Friday?

Question

across · Answer

Let $H$ stand for hamburgers and $C$ for cheeseburgers.

The first sentence tells us that$$H+C=600.$$The second sentence tells us that$$C=H+50.$$This is a system of two equations. Do you know how to solve it?

across · Answer

Solve for $H$, that is.

anonymous · Answer

550 for the first one? not really sure =/

across · Answer

Let’s walk through it. :)

We came up with the following system:$$H+C=600,$$$$C=H+50.$$Since we want to solve for $H$, let’s first rearrange the first equation a little bit (with the intent of solving for $H$):$$H=600-C.$$Are you with me thus far?

anonymous · Answer

yea

across · Answer

We now have the following system:$$H=600-C,$$$$C=H+50.$$Since we still want to find $H$, we want to get rid of $C$. Effectively enough, the second equation tells us what $C$ is. We now plug it into the first equation, as follows:$$H=600-[H+50].$$Are you still with me?

anonymous · Answer

not really =/

across · Answer

Let me break it down for you into two steps:

1. We ended up with the following system:$$H=600-C,$$$$C=H+50.$$2. We want to solve for $H$, so we want to get rid of $C$. The first equation has a $C$ on the right hand side, and from the second equation, we know that $C=H+50$. So we basically “plug” the second equation into the first one, like this:
$$H=600-C\implies H=600-(H+50)$$(since $C=H+50$).

anonymous · Answer

can you please provide the answer pls i'm so lost with this

across · Answer

Okay…

… all we have to do now is simplify the last expression we obtained:$$H=600-(H+50)$$$$\implies H=600-H-50$$$$\implies2H=550$$$$\implies H= 275.$$That’s how many hamburgers were sold.

anonymous · Answer

Alright thanks so much!