18. Alex needs \( 5 \frac{1}{3} \) cups of ginger ale to make punch for a group of her friends. She has only \( 2 \frac{1}{2} \) cups. Write an equation to represent how many more cups of ginger ale Alex needs. Then solve. Select the correct equation that represents the problem. A. \( c=2 \frac{1}{2}+5 \frac{1}{3} \) B. \( 2 \frac{1}{2}=5 \frac{1}{3}+c \) C. \( 2 \frac{1}{2}-c=5 \frac{1}{3} \) How many more cups does Alex need? \( 2 \frac{1}{2}+\mathrm{c}=5 \frac{1}{3} \) Alex needs \( \square \) more cup(s) of ginger ale. (Type a whole number, fraction, or mixed number.) View an example \( \quad \) Video Get more help -

To find out how many more cups of ginger ale Alex needs, we need to set up an equation that represents the situation. Let \( c \) be the number of cups of ginger ale Alex needs to make punch for her friends. Given: - Alex needs \( 5 \frac{1}{3} \) cups of ginger ale. - Alex has \( 2 \frac{1}{2} \) cups of ginger ale. The equation to represent how many more cups of ginger ale Alex needs is: \[ 2 \frac{1}{2} + c = 5 \frac{1}{3} \] Now, we need to solve this equation to find out how many more cups of ginger ale Alex needs. Let's solve the equation step by step. Solve the equation by following steps: - step0: Solve for \(c\): \(2\frac{1}{2}+c=5\frac{1}{3}\) - step1: Convert the expressions: \(\frac{5}{2}+c=\frac{16}{3}\) - step2: Move the constant to the right side: \(c=\frac{16}{3}-\frac{5}{2}\) - step3: Subtract the numbers: \(c=\frac{17}{6}\) The solution to the equation \(2 \frac{1}{2} + c = 5 \frac{1}{3}\) is \(c = \frac{17}{6}\) or \(c = 2.8\dot{3}\). Therefore, Alex needs \(2.8\dot{3}\) more cups of ginger ale.