NEXT BOOKMARK Each chef at “Sushi Emperor” restaurant prepares 15 regular sushi rolls and 20 vegetarian sushi rolls daily: On Tuesday; each customer ate 2 regular rolls and 3 vegetarian rolls: At the end of the day, 4 regular rolls and 1 vegetarian roll remained uneaten How many chefs and how many customers were in “Sushi Emperor’ on Tuesday? There were chefs and customers’
The Correct Answer and Explanation is:
To solve this problem, let’s break down the information step by step:
Step 1: Define Variables
Let:
- ccc be the number of chefs working on Tuesday.
- nnn be the number of customers who visited the restaurant.
Step 2: Roll Preparation
Each chef prepares 15 regular sushi rolls and 20 vegetarian rolls every day. Therefore, the total number of rolls prepared by ccc chefs is:
- Regular rolls: 15c15c15c
- Vegetarian rolls: 20c20c20c
Step 3: Rolls Consumed by Customers
Each customer eats 2 regular rolls and 3 vegetarian rolls. Thus, the total number of rolls consumed by nnn customers is:
- Regular rolls: 2n2n2n
- Vegetarian rolls: 3n3n3n
Step 4: Leftover Rolls
At the end of the day, there are 4 regular rolls and 1 vegetarian roll left uneaten. This means the total rolls prepared minus the rolls consumed equals the leftover rolls:
- Regular rolls: 15c−2n=415c – 2n = 415c−2n=4
- Vegetarian rolls: 20c−3n=120c – 3n = 120c−3n=1
Step 5: Solve the System of Equations
We now have the system of two equations:
- 15c−2n=415c – 2n = 415c−2n=4
- 20c−3n=120c – 3n = 120c−3n=1
To solve this, let’s start by multiplying the first equation by 3 and the second equation by 2 to eliminate nnn:3(15c−2n)=3(4)⇒45c−6n=123(15c – 2n) = 3(4) \quad \Rightarrow \quad 45c – 6n = 123(15c−2n)=3(4)⇒45c−6n=122(20c−3n)=2(1)⇒40c−6n=22(20c – 3n) = 2(1) \quad \Rightarrow \quad 40c – 6n = 22(20c−3n)=2(1)⇒40c−6n=2
Now subtract the second equation from the first:(45c−6n)−(40c−6n)=12−2(45c – 6n) – (40c – 6n) = 12 – 2(45c−6n)−(40c−6n)=12−25c=105c = 105c=10c=2c = 2c=2
Step 6: Find nnn
Substitute c=2c = 2c=2 into the first equation:15(2)−2n=4⇒30−2n=415(2) – 2n = 4 \quad \Rightarrow \quad 30 – 2n = 415(2)−2n=4⇒30−2n=4−2n=−26⇒n=13-2n = -26 \quad \Rightarrow \quad n = 13−2n=−26⇒n=13
Step 7: Conclusion
Thus, there were 2 chefs and 13 customers in the restaurant on Tuesday.
This solution satisfies both the total number of rolls prepared and the number of rolls consumed, while accounting for the leftovers at the end of the day.
