Two friends are making lemonade to sell at their lemonade stand. First, they make 4 liters of lemonade containing 31% lemon juice, but that doesn't taste quite right to them. They decide to add some store-bought lemonade that is 26% lemon juice until they have a mixture that is 27% lemon juice. How much of the store-bought lemonade should they add? Write your answer as a whole number or as a decimal rounded to the nearest tenth. ____ liters

Question

Two friends are making lemonade to sell at their lemonade stand. First, they make 4 liters of lemonade containing 31% lemon juice, but that doesn't taste quite right to them. They decide to add some store-bought lemonade that is 26% lemon juice until they have a mixture that is 27% lemon juice. How much of the store-bought lemonade should they add? Write your answer as a whole number or as a decimal rounded to the nearest tenth.   ____ liters

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Calculate Lemon Juice Amount: Determine the amount of lemon juice in the initial 4 liters of lemonade. Calculation: 4 liters × 31% = 4 × 0.31Determine Lemon Juice in Mixture: Calculate the amount of lemon juice in the initial mixture. Calculation: 4 liters × 0.31 = 1.24 liters of lemon juiceFind Store-Bought Lemonade Amount: Let x be the amount of store-bought lemonade (in liters) that needs to be added. Expression: x liters of store-bought lemonadeCalculate Total Lemon Juice: Determine the amount of lemon juice in the store-bought lemonade that will be added. Expression: x liters × 26% = x × 0.26Set Up Equation: Set up an equation for the total amount of lemon juice in the final mixture. Expression: 1.24 liters (from initial mixture) + x × 0.26 (from store-bought lemonade) = (4 liters + x) × 27%Convert Percentage to Decimal: Convert the percentage to a decimal and set up the equation. Equation: 1.24 + x × 0.26 = (4 + x) × 0.27Distribute Equation: Distribute the 0.27 on the right side of the equation. Equation: 1.24 + 0.26x = 4 × 0.27 + x × 0.27Calculate Lemon Juice in Final Mixture: Calculate the amount of lemon juice in the 4 liters of the final mixture. Calculation: 4 × 0.27 = 1.08 liters of lemon juiceSubstitute Calculated Amount: Substitute the calculated amount into the equation. Equation: 1.24 + 0.26x = 1.08 + 0.27xRearrange Equation: Rearrange the equation to isolate x on one side. Equation: 0.26x - 0.27x = 1.08 - 1.24Simplify Equation: Simplify the equation. Equation: -0.01x = -0.16Solve for x: Solve for x, which represents the liters of store-bought lemonade to be added. Calculation: x = (-0.16) / (-0.01)Calculate x Value: Calculate the value of x. Calculation: x = 16 liters

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