7. At a fall festival, a student council sold two types of drinks: hot chocolate and apple cider. The student council earned $2 for every cup of hot chocolate it sold and $1 for every cup of apple cider it sold. There were
375 cups of drinks sold, and the total amount of money earned from selling drinks were $400.
The system of equations shown can be used to represent the situation.
x + y = 375
2x + y = 400

Remark

There are two ways to do this. You can graph the equations (which I have included at the end of the question using Desmos) or you can solve it algebraically which in this case is going to be slightly painful.

Algebra

Multiply the first equation by 4 and the second by 3

First Equation

4 [3x + 4y = 16]

12x + 16y = 64             (3)

Second Equation

3 [-4x - 3y = - 19]

- 12x - 9y = - 57           (4)

Add (3) and (4)

12x + 16y = 64

- 12x - 9y = -57           Add

7y = 7                           Divide by 7

y = 1

Solve for x

3x + 4y = 16         Let y = 1

3x + 4(1) = 16

3x + 4 = 16           Subtract 4

3x = 12                 Divide by 3

x = 12/3

x = 4

Answer

(4,1) just as the graph suggests.