you sell lemonade for $2 per cup and orange juice for $3 per cup. You sell a total of 100 cups for $240. Write and solve a system of linear equations to find the number of cups of lemonade and the number of cups of orange juice you sold. Solve using substitution.

First write the given information from the problem: $2 = amount of lemonade per cup $3 = amount of orange juice per cup 100 cups = total cups sold $240 = total amount sold By representation we can write : x = number of cups of lemonade sold 100 - x = number of cups of orange juice sold So in forming the linear equation we write the following: $2x + $3(100 - x) = $240 2x + 300 - 3x = 240 (by distributing the term with 100 - x) - 1x + 300 = 240 (by adding like terms 2x and - 3x) -1x = 240 - 300 (by transposing 300 to the left side of the equation) -1x = - 60 (by subtracting 240-300) x = 60 (by diving the right side and left side of the equation by -1) so now we know that there are 60 cups of the lemonade sold, and to find the number of cups of the orange juice sold we perform : 100 - x = 100 - 60 = 40 cups of orange juice sold. We ca check if our answers are correct by performing the original linear equation 2x + 3(100 - x) = 240 2(60) + 3 (100-60) = 240 120 + 3(40) = 240 120 + 120 =240 240 = 240 so our answers are correct since it gives the correct total amount sold of 240