Each chef at "sushi emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. on tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. by the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten. how many chefs and how many customers were in "sushi emperor" on tuesday?

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 tuesdaySolution: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 dailyIf each chef prepares 15 regular rolls, then x chefs prepare 15x regular rollsIf each customer ate 2 regular rolls, then y customers ate 2y regular rollsBy the end of the day, 4 regular roll remained un eatingTherefore,15x - 2y = 4 --------- eqn 1If each chef prepares 20 vegetarian rolls, then x chefs prepare 20x vegetarian rollsIf each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rollsBy the end of the day, 1 vegetarian roll remained uneatingTherefore,20x - 3y = 1 ---------- eqn 2Let us solve eqn 1 and eqn 2Multiply eqn 1 by 345x - 6y = 12 ------- eqn 3Multiply eqn 2 by 240x - 6y = 2 ------- eqn 4Subtract eqn 4 from eqn 345x - 6y = 1240x - 6y = 2( - ) --------------5x = 10x = 2Substitute x = 2 in eqn 120(2) - 3y = 140 - 3y = 13y = 39y = 13Thus there were 2 chefs and 13 customers