You sell lemonade for $2 per cup and orange juice for $3 per cup. you sell a total of 100 cups for $ 240. how many cups of lemonade and orange juice were sold ?

Lemonade:
From the given information,you can write an linear equation like this:
$2x + $3(100 - x) = 240
First, you have to distribute them = 2x + 300 - 3x 
Then, you have to add like terms = 1x + 300=240
Next, you have to transpose 300 to the left = -1x = 300 - 240
So, you have to subtract = -1x = -60
And, you solve = -60 = -60 So x = 60
60 cups of lemonade sold

Orange:
100 - x = 100 - 60 = 40 cups of orange juice sold
So you can check our answer by using the original linear equation
2x + 3( 100 - x) = 240 2(60) + 3 (100 - 60) = 240 120 + 3(40) = 240 120 + 120 = 240 240 = 240

Hope this helps! ;)