1.
Let the sandwich be represented by = x
Let the drink be represented by = y
As given, Joe charges $10.00 for two sandwiches and one drink, so equation becomes 2x+y=10 ....(i)
He charges $6.50 for one sandwich and one drink, so equation becomes x+y=6.50 ....(ii)
Subtracting (ii) from (i) we get
x=3.50
And as x+y=6.50
y=6.50-3.50=3.00
Hence, cost of a sandwich is $3.50 and a drink is $3.00
2.
the question is incomplete. coordinates are missing
3.
Let x represent the number of performances
cost = 8000+300x
revenue = 700x
To break even, the cost must be equal to the revenue.
![8000+300x=700x](https://tex.z-dn.net/?f=8000%2B300x%3D700x)
![400x=8000](https://tex.z-dn.net/?f=400x%3D8000)
so x=20
Hence, 20 performances are needed to break even.
4.
Let us take x for 20% material, y for 50% material
![\frac{20x+50y}{200}=30](https://tex.z-dn.net/?f=%5Cfrac%7B20x%2B50y%7D%7B200%7D%3D30)
......... (1)
Accounting for volumes to use, x+y=200 or x=200-y ................ (2)
Putting the value of x in (1)
![20(200-y)+50y=6000](https://tex.z-dn.net/?f=20%28200-y%29%2B50y%3D6000)
![4000-20y+50y=6000](https://tex.z-dn.net/?f=4000-20y%2B50y%3D6000)
![4000+30y=6000](https://tex.z-dn.net/?f=4000%2B30y%3D6000)
![30y=2000](https://tex.z-dn.net/?f=30y%3D2000)
y=66.67
x=200-y = 200-66.67 =133.33
Hence, 133.33 ml of 20% acetic acid and 66.67% of 50% acetic acid is needed.