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.

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Step-by-step explanation:

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

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