Three different chefs work together to prepare meals for 280 dinner guests. Each works at a different speed, and their combined output throughout the night is modeled by the equation 8x + 4x + 2x = 280. If x is a positive integer, which of the following could 8x represent in the equation?
A. The total meal output by the slowest chef, who made 40 meals.
B. The total meal output by the fastest chef, who made 160 meals.
C. The total meal output by the fastest chef, who made 80 meals.
D. The difference between the output between the slowest and fastest chef, which would be 120 meals.
Answer:B
Three different chefs work together to prepare meals for 280 dinner guests. Each works at a different speed, and their combined output throughout the night is modeled by the equation 8x + 4x + 2x = 280. If x is a positive integer, which of the following could 8x represent in the equation?
A. The total meal output by the slowest chef, who made 40 meals. B. The total meal output by the fastest chef, who made 160 meals. C. The total meal output by the fastest chef, who made 80 meals. D. The difference between the output between the slowest and fastest chef, which would be 120 meals.
Explanation: B Since work = rate × time, the 280 in the equation must represent the total number of meals (i.e. the "work"). All three chefs are working together, so they work for the same amount of time, and x must represent that time. The coefficients 8, 4, and 2 must therefore represent the chefs' respective rates, or how many meals each prepares in a set amount of time. Since 8 is the greatest of these three coefficients, 8x must be the meal output of the fastest chef, either (B) or (C). Now you need to solve the equation: 8x + 4x + 2x = 280. Combining like terms gives you 14x = 280. Divide both sides by 14 to determine that x = 20. This number represents the amount of time that the chefs worked, so the actual number of meals prepared by the fastest chef would be 8 × 20 = 160 meals, which is (B).