Question

marco and elena are selling lemonade at their local fair. marco has already sold 92 cups of lemonade and sells an additional 9 cups every hour. elena has only sold 83 cups so far but is selling 12 cups each hour because of her booth’s location. after how many hours will elena have sold at least as many cups of lemonade as marco? let ( x ) represent the number of hours marco and elena will sell lemonade. write an inequality to represent the situation. then solve the inequality. use the keypad to enter the answer in the boxes. an inequality to represent the situation is (square). elena will sell at least as many cups of lemonade as marco after (square) hours.

Explanation:

Step1: Define total cups for each

Elena's total: $83 + 12x$; Marco's total: $92 + 9x$

Step2: Set up inequality

Elena's total ≥ Marco's total:
$$83 + 12x \geq 92 + 9x$$

Step3: Isolate x terms

Subtract $9x$ from both sides:
$$83 + 3x \geq 92$$

Step4: Isolate constant terms

Subtract 83 from both sides:
$$3x \geq 9$$

Step5: Solve for x

Divide by 3:
$$x \geq 3$$

Answer:

An inequality to represent the situation is $\boldsymbol{83 + 12x \geq 92 + 9x}$.
Elena will sell at least as many cups of lemonade as Marco after $\boldsymbol{3}$ hours.