Question

select the correct answer. joe and will both work as cooks at burger palace. each prepares hamburgers at a different speed, as shown by the functions below: $j(b) = 14b + 7$ $w(b) = 7b + 42$ where $b$ represents the number of hamburgers cooked and $j(b)$ and $w(b)$ represent the amount of time each cook takes in minutes. at what value of $b$ will their cooking time be equivalent? \\(\bigcirc\\) a. $b = 5$ \\(\bigcirc\\) b. $b = 19$ \\(\bigcirc\\) c. $b = 6$ \\(\bigcirc\\) d. $b = 12$

Explanation:

Step1: Set the two functions equal

To find when their cooking times are equivalent, set \( J(b) = W(b) \), so \( 14b + 7 = 7b + 42 \).

Step2: Subtract \( 7b \) from both sides

\( 14b - 7b + 7 = 7b - 7b + 42 \), which simplifies to \( 7b + 7 = 42 \).

Step3: Subtract 7 from both sides

\( 7b + 7 - 7 = 42 - 7 \), resulting in \( 7b = 35 \).

Step4: Divide both sides by 7

\( \frac{7b}{7} = \frac{35}{7} \), so \( b = 5 \).

Answer:

A. \( b = 5 \)