question 6 of 10: your catering business sells luncheons and dinners. luncheons are $1,000 each, and dinners…

question 6 of 10: your catering business sells luncheons and dinners. luncheons are $1,000 each, and dinners are $2,000 each. you sold 300 meals in total for revenue of $460,000. how many of each did you sell?\na) 100 luncheons, 200 dinners\nb) 120 luncheons, 180 dinners\nc) 140 luncheons, 160 dinners\nd) 200 luncheons, 100 dinners

question 6 of 10: your catering business sells luncheons and dinners. luncheons are $1,000 each, and dinners are $2,000 each. you sold 300 meals in total for revenue of $460,000. how many of each did you sell?\na) 100 luncheons, 200 dinners\nb) 120 luncheons, 180 dinners\nc) 140 luncheons, 160 dinners\nd) 200 luncheons, 100 dinners

Answer

Explanation:

Step1: Set up equations

Let $x$ be the number of luncheons and $y$ be the number of dinners. We have two - equations: $x + y=300$ (total number of meals) and $1000x + 2000y=460000$ (total revenue). From the first equation, we get $x = 300 - y$.

Step2: Substitute into revenue equation

Substitute $x = 300 - y$ into $1000x+2000y = 460000$. So $1000(300 - y)+2000y=460000$. Expand to get $300000-1000y + 2000y=460000$. Combine like - terms: $1000y=460000 - 300000$, so $1000y = 160000$.

Step3: Solve for $y$

Divide both sides of $1000y = 160000$ by 1000, we get $y=\frac{160000}{1000}=160$.

Step4: Solve for $x$

Substitute $y = 160$ into $x = 300 - y$, we get $x=300 - 160 = 140$.

Answer:

C. 140 luncheons, 160 dinners