You sell lemonade for $2 and orange juice for $3. You sell 100 cups for $240. How many cups of lemonade and how many cups of orange juice were sold

L + O = 100 or L = 100 - O

2L + 3O = 240
substitute first equation into second equation:
2(100 - O) + 3O = 240
200 - 2O + 3O = 240
O = 40 cups
using first equation:
L = 100 - 40 = 60 cups
check using second equation:
2(60) + 3(40) = 240
120 + 120 = 240 checks
Sold 40 cups of orange juice and 60 cups of lemonade.

Let total no. of lemonade and orange juice cups sold be x and y respectively.

x+y=100
2x+3y=240

Solve for x and y :)

Let's assume that the number of cups of lemonade sold is represented by 'x' and the number of cups of orange juice sold is represented by 'y'.

According to the given information, the selling price of lemonade is $2, and the selling price of orange juice is $3. We can set up the following equations based on the total sales:

1. Price of lemonade * number of cups of lemonade = Total sales from lemonade
2x = Total sales from lemonade

2. Price of orange juice * number of cups of orange juice = Total sales from orange juice
3y = Total sales from orange juice

3. Total sales from lemonade + Total sales from orange juice = Total sales
2x + 3y = 240

We also know that the total number of cups sold is 100, so we can set up the following equation:

4. Number of cups of lemonade + Number of cups of orange juice = Total cups sold
x + y = 100

We can solve this system of equations using substitution or elimination method.

Let's solve this system using the elimination method:
Multiply equation 4 by 2 to eliminate the variable x:
2(x + y) = 2(100)
2x + 2y = 200 (equation 5)

Now subtract equation 5 from equation 3 to eliminate x:
(2x + 3y) - (2x + 2y) = 240 - 200
2x + 3y - 2x - 2y = 40
y = 40

Substitute the value of y = 40 into equation 4:
x + 40 = 100
x = 100 - 40
x = 60

Therefore, 60 cups of lemonade and 40 cups of orange juice were sold.

To find the number of cups of lemonade and orange juice sold, we need to set up a system of equations.

Let's say the number of cups of lemonade sold is L, and the number of cups of orange juice sold is O.

According to the given information, the price of lemonade is $2, and the price of orange juice is $3.

From the first sentence, we know that the total revenue from selling 100 cups is $240. Therefore, we can write the equation:

2L + 3O = 240

Since we want to find the values of L and O, we need another equation. This equation will reflect the total number of cups sold:

L + O = 100

Now we have a system of two equations:

2L + 3O = 240
L + O = 100

We can solve this system of equations using various methods. One common method is substitution. Rearrange the second equation to solve for one variable in terms of the other. For example:

L = 100 - O

Substitute this value of L into the first equation:

2(100 - O) + 3O = 240

Simplify and solve for O:

200 - 2O + 3O = 240
200 + O = 240
O = 240 - 200
O = 40

Now substitute this value of O back into the second equation to find L:

L + 40 = 100
L = 100 - 40
L = 60

Therefore, 60 cups of lemonade and 40 cups of orange juice were sold.