Question

A) Mr. Bernie sold hamburgers where each hamburger patty weighed
1
3
pound. The total weight in
pounds of the meat on a hamburger with n patties can be found using the model
b(n) =
1
3
+ (n − 1)
1
3
. Use the model to find the number of burger patties that would be on a
hamburger whose meat weighs
5
3
pounds. (1 point)
1
2
3
hamburger patties
5
9
pounds
5 pounds
5 hamburger patties

Answer 1

The model given for the total weight of the meat on a hamburger with \( n \) patties is:

\[
b(n) = \frac{1}{3} + (n - 1) \cdot \frac{1}{3}
\]

We can simplify this expression:

\[
b(n) = \frac{1}{3} + \frac{(n - 1)}{3} = \frac{1 + (n - 1)}{3} = \frac{n}{3}
\]

Now, we want to find the number of patties \( n \) when the weight of the meat is \( \frac{5}{3} \) pounds. Thus, we set up the equation:

\[
b(n) = \frac{5}{3}
\]

Substituting the simplified expression:

\[
\frac{n}{3} = \frac{5}{3}
\]

To solve for \( n \), we multiply both sides by 3:

\[
n = 5
\]

Thus, the number of burger patties that would be on a hamburger whose meat weighs \( \frac{5}{3} \) pounds is \( \boxed{5} \).