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:

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