At Carl’s Diner ,there are 3 sizes of coffee drinks: regular (300 ml), large(500ml) and
extra – large (800ml), and they cost Rs. 5 , Rs.8 and Rs.12 respectively. One evening
the diner sold a total of 37 coffees. The total volume of coffee sold was 19,100ml and the
amount of money made in coffee sales was Rs. 300. How many, of each size of drink,
did customers buy that evening? (Using Cramer’s rule)
Answers
Given : At Carl's Diner ,there are 3 sizes of coffee drinks: regular (300 ml), large(500ml) and extra - large (800ml), and they cost Rs. 5. Rs.8 and Rs.12 respectively.
One evening the diner sold a total of 37 coffees The total volume of coffee sold was 19,100ml and the amount of money made in coffee sales was Rs. 300.
To Find : How many, of each size of drink, did customers buy that evening
Solution:
x = 300 ml cup
y = 500 ml cup
z = 800 ml cup
x + y + z = 37
300x + 500y + 800z = 19100
=> 3x + 5y + 8z = 191
5x + 8y + 12z = 300
3x + 3y + 3z = 111
3x + 5y + 8z = 191
=> 2y + 5z = 80
5x + 8y + 12z = 300
5x + 5y + 5z = 185
=> 3y + 7z = 115
2y + 5z = 80 => 6y + 15z = 240
3y + 7z = 115 => 6y + 14z = 230
=> z = 10
2y + 5z = 80
=> 2y + 50 = 80
=> 2y = 30
=> y = 15
x + y + z = 37
=> x + 15 + 10 = 37
=> x = 12
12 cups of 300 ml
15 cups of 500 ml
10 cups of 800 ml
Cramer rule
x + y + z = 37
3x + 5y + 8z = 191
5x + 8y + 12z = 300
=> x = -12/-1 = 12
=> y = -15/-1 = 15
=> z = -10/-1 = 10
12 cups of 300 ml
15 cups of 500 ml
10 cups of 800 ml
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