A local hamburger shop sold a combined total of 437 hamburgers and cheeseburgers on Wednesday. There were 63 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?

Answer 1

Let \( h \) represent the number of hamburgers sold and \( c \) represent the number of cheeseburgers sold.

We have the following two equations based on the problem statement:

1. The total number of hamburgers and cheeseburgers sold is 437: \[ h + c = 437 \]

2. There were 63 fewer cheeseburgers sold than hamburgers: \[ c = h - 63 \]

Now, we can substitute the expression for \( c \) from the second equation into the first equation:

\[ h + (h - 63) = 437 \]

Simplifying this, we combine like terms:

\[ 2h - 63 = 437 \]

Next, we add 63 to both sides to isolate the term with \( h \):

\[ 2h = 437 + 63 \] \[ 2h = 500 \]

Now, we divide both sides by 2 to solve for \( h \):

\[ h = \frac{500}{2} = 250 \]

Thus, the number of hamburgers sold on Wednesday is \( h = 250 \).

We can double-check our solution by calculating the number of cheeseburgers sold:

Using the second equation \( c = h - 63 \): \[ c = 250 - 63 = 187 \]

Now, let’s verify that the totals match: \[ h + c = 250 + 187 = 437 \]

This is true, confirming our solution is correct. Therefore, the number of hamburgers sold on Wednesday is

\[ \boxed{250} \]