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. \( 2 \frac{1}{2}-c=5 \frac{1}{3} \) D. \( 2 \frac{1}{2}+c=5 \frac{1}{3} \) View an example \( \quad \) Video Get more help -

To find out how many more cups of ginger ale Alex needs, we want to see how much she still needs after using what she currently has. Thus, the equation should be structured to represent the total needed minus what she has. In this case, the correct choice is option D: \( 2 \frac{1}{2} + c = 5 \frac{1}{3} \). Now, let's solve for \( c \). Start by converting the mixed numbers to improper fractions. \( 2 \frac{1}{2} = \frac{5}{2} \) and \( 5 \frac{1}{3} = \frac{16}{3} \). The equation then becomes \( \frac{5}{2} + c = \frac{16}{3} \). To find \( c \), subtract \( \frac{5}{2} \) from \( \frac{16}{3} \). Finding a common denominator (which is 6) gives us \( c = \frac{32}{6} - \frac{15}{6} = \frac{17}{6} \). Thus, Alex needs \( \frac{17}{6} \) cups, or 2 and \( \frac{5}{6} \) cups more of ginger ale. Now, isn't it fascinating how fractions can tell us just as much about our cooking adventures as they do about math? Whether you're concocting delightful punch or just measuring out ingredients for a cake, the meticulous balance of numbers can transform a simple recipe into a perfect treat for your friends. You're basically a mathematical chef! And let's not forget, in the world of cooking and mixing drinks, precise measurements can make or break a recipe. Always double-check your measurements and conversions! Mixing those fractions, whether they are cups or spoons, can be tricky. One common mistake is forgetting to properly convert mixed numbers to improper fractions before performing operations. Don’t let small oversights spoil your big bash!