Question

Iced tea and lemonade sell for different prices per gallon at Chicken-Fill-Up. Two gallons of iced tea and 3 gallons of lemonade cost a total of $23.25. Five gallons of iced tea and 4 gallons of lemonade cost a total of $41.50. What is the price per gallon for each drink at Chicken-Fill-Up? What equation would I use to find the answer?

Answer 1

• Iced tea is $4.50 per gallon
• Lemonade is $4.75 per gallon

Explanation:

Price:

• Iced tea = x, lemonade = y

Equations:

• 2x + 3y = 23.25
• 5x + 4y = 41.50

Multiply the first equation by 5 and the second equation by 2 and subtract to eliminate x:

• 5(2x + 3y) - 2(5x + 4y) = 5(23.25) - 2(41.50)
• 10x + 15y - 10x - 8y = 33.25
• 7y = 33.25
• y = 33.25/7
• y = 4.75

Use the first equation to find x:

• 2x + 3(4.75) = 23.25
• 2x = 23.25 - 14.25
• 2x = 9
• x = 9/2
• x = 4.50

Iced tea costs $4.50 per gallon

Lemonade costs $4.75 per gallon