Question

hotdog eating contest
minutes | hotdogs
1 | x
4 | 24
y | 42

Explanation:

To solve for \( x \) (hotdogs eaten in 1 minute) and \( y \) (minutes to eat 42 hotdogs), we assume a constant rate of hotdog eating (proportional relationship).

Step 1: Find the rate (\( x \))

In 4 minutes, 24 hotdogs are eaten. The rate \( x \) (hotdogs per minute) is:
\[
x = \frac{\text{Hotdogs}}{\text{Minutes}} = \frac{24}{4}
\]
Simplify:
\[
x = 6
\]

Step 2: Find \( y \) (minutes for 42 hotdogs)

Using the rate \( x = 6 \) hotdogs per minute, we solve for \( y \) when hotdogs = 42:
\[
\text{Rate} = \frac{42}{y} \implies 6 = \frac{42}{y}
\]
Multiply both sides by \( y \):
\[
6y = 42
\]
Divide by 6:
\[
y = \frac{42}{6} = 7
\]

Answer:

\( x = 6 \), \( y = 7 \)