Respuesta :
Question:
Each chef at "sushi emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On tuesday, each customer ate 2 regular rolls & 3 vegetarian rolls. by the end of the day, 4 regular rolls & 1 vegetarian roll remained uneating. how many chefs were on tuesday ? and how many customers were they ?
Answer:
There were 2 chefs and 13 customers on tuesday
Solution:
Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday.
From given,
Each chef prepares 15 regular rolls and 20 vegetarian rolls daily
If each chef prepares 15 regular rolls, then x chefs prepare 15x regular rolls
If each customer ate 2 regular rolls, then y customers ate 2y regular rolls
By the end of the day, 4 regular roll remained un eating
Therefore,
15x - 2y = 4 --------- eqn 1
If each chef prepares 20 vegetarian rolls, then x chefs prepare 20x vegetarian rolls
If each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rolls
By the end of the day, 1 vegetarian roll remained uneating
Therefore,
20x - 3y = 1 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 3
45x - 6y = 12 ------- eqn 3
Multiply eqn 2 by 2
40x - 6y = 2 ------- eqn 4
Subtract eqn 4 from eqn 3
45x - 6y = 12
40x - 6y = 2
( - ) --------------
5x = 10
x = 2
Substitute x = 2 in eqn 1
20(2) - 3y = 1
40 - 3y = 1
3y = 39
y = 13
Thus there were 2 chefs and 13 customers
