Answer:
The number of regular, large, and extra-large drinks are 12, 15, and 10 respectively.
Step-by-step explanation:
Given that the cost for regular coffee drinks (300 ml)=$2.25
The cost for large coffee drinks (500 ml)=$3.25
The cost for extra large coffee drinks (800 ml)=$5.75
Let p,q, and r be the number of regular, large, and extra-large coffee sold.
As the diner sold a total of 37 coffees, so
p+q+r=37
r=37-p-q...(i)
The volume of p regular coffee = 300p ml
The volume of q large coffee = 500q ml
The volume of r extra-large coffee = 800r ml
As the total volume of coffee sold was 19,100mi, so
300p+500q+800r=19100
By using equation (i)
300p+500q+800(37-p-q)=19100
300p+500q+800 x 37 - 800p - 800q=19100
-500p-300q=19100-29600
500p+300q=10500
500p=10500-300q
p=21-0.6q...(ii)
Now, the cost of p regular coffee=$2.25p
The cost of q large coffee=$3.25q
The cost of r extra-large coffee=$5.75r
As the amount of money made in coffee sales was $133.25, so
2.25p+3.25q+5.75r=133.25
By using equations (1) we have
2.25p+3.25q+5.75(37-p-q)=133.25
2.25p+3.25q+212.75-5.75p-5.75q=133.25
3.50p+2.50q=79.5
From equation (ii)
3.5(21-0.6q)+2.50q=79.5
73.5-2.1q+2.5q=79.5
0.4q=79.5-73.5=6
q=6/0.4
q=15
From equation (ii)
p=21-0.6(15)
p=12
From equation (i)
r= 37-12-15
r=10
Hence, the number of regular, large, and extra-large drinks are 12, 15, and 10 respectively.
![\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=-\cfrac{3}{10}[x-(-5)] \\\\\\ y-2=-\cfrac{3}{10}(x+5)\implies y-2=-\cfrac{3}{10}x-\cfrac{3}{2}\implies y=-\cfrac{3}{10}x-\cfrac{3}{2}+2 \\\\\\ y=-\cfrac{3}{10}x+\cfrac{1}{2}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bpoint-slope%20form%7D%7D%7By-%7B%7B%20y_1%7D%7D%3D%7B%7B%20m%7D%7D%28x-%7B%7B%20x_1%7D%7D%29%7D%5Cimplies%20y-2%3D-%5Ccfrac%7B3%7D%7B10%7D%5Bx-%28-5%29%5D%0A%5C%5C%5C%5C%5C%5C%0Ay-2%3D-%5Ccfrac%7B3%7D%7B10%7D%28x%2B5%29%5Cimplies%20y-2%3D-%5Ccfrac%7B3%7D%7B10%7Dx-%5Ccfrac%7B3%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B3%7D%7B10%7Dx-%5Ccfrac%7B3%7D%7B2%7D%2B2%0A%5C%5C%5C%5C%5C%5C%0Ay%3D-%5Ccfrac%7B3%7D%7B10%7Dx%2B%5Ccfrac%7B1%7D%7B2%7D)
