Question

Diego ran a lemonade stand where he sold small cups of lemonade for $1 and large cups for $3.00. Diego sold a total of 75 cups of lemonade. If he collected a total of $125, how many cups of each size did Diego sell?​

Answer 1

To solve this problem, set up a system of equations using the number of small cups and large cups Diego sold. Solve the system using elimination or substitution to find the values of x and y. Diego sold 50 small cups and 25 large cups of lemonade.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's assume that Diego sold x small cups and y large cups. We can then set up the following two equations:

1x + 3y = 125 (equation 1)

x + y = 75 (equation 2)

We can solve this system of equations using either substitution or elimination. Let's use elimination. First, multiply equation 2 by -1:

-x - y = -75

Now, add equation 1 and -x - y:

1x - x + 3y - y = 125 - 75

Simplifying, we get:

2y = 50

Dividing both sides of the equation by 2, we find that y = 25. Now, substitute this value back into equation 2 to find x:

x + 25 = 75

Subtracting 25 from both sides, we get:

x = 50

Therefore, Diego sold 50 small cups and 25 large cups of lemonade.