Questions: Manny prepared 15.9 kilograms of dough after working 4 hours. How many hours did Manny work if he prepared 31.8 kilograms of dough? Assume the relationship is directly proportional.

Solution Steps

To solve this problem, we can use the concept of direct proportionality. Since the amount of dough prepared is directly proportional to the number of hours worked, we can set up a proportion to find the unknown number of hours. Specifically, we can use the ratio of dough to hours for the known values and set it equal to the ratio for the unknown values.

Given that the relationship between the amount of dough prepared and the hours worked is directly proportional, we can express this relationship as: \[ \frac{dough_1}{hours_1} = \frac{dough_2}{hours_2} \] Substituting the known values: \[ \frac{15.9}{4} = \frac{31.8}{hours_2} \]

To find \( hours_2 \), we can cross-multiply: \[ 15.9 \cdot hours_2 = 31.8 \cdot 4 \] This simplifies to: \[ 15.9 \cdot hours_2 = 127.2 \] Now, divide both sides by \( 15.9 \): \[ hours_2 = \frac{127.2}{15.9} \]

Calculating the value gives: \[ hours_2 = 8.0 \]

Final Answer