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 -

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UpStudy AI · Accepted Answer

To determine how many more cups of ginger ale Alex needs, let's analyze the problem step by step.

**Given:**
- **Total cups needed:** $$ 5 \frac{1}{3} $$ cups
- **Cups Alex already has:** $$ 2 \frac{1}{2} $$ cups

Let $$ c $$ represent the additional cups of ginger ale Alex needs.

**Setting Up the Equation:**
Alex's current amount plus the additional cups should equal the total cups needed. This can be expressed as:

$$
2 \frac{1}{2} + c = 5 \frac{1}{3}
$$

**Therefore, the correct equation is:**

**D. $$ 2 \frac{1}{2} + c = 5 \frac{1}{3} $$**

---

**Solving the Equation:**

1. **Convert mixed numbers to improper fractions:**
   $$
   2 \frac{1}{2} = \frac{5}{2}
   $$
   $$
   5 \frac{1}{3} = \frac{16}{3}
   $$

2. **Set up the equation with improper fractions:**
   $$
   \frac{5}{2} + c = \frac{16}{3}
   $$

3. **Subtract $$ \frac{5}{2} $$ from both sides to solve for $$ c $$:**
   $$
   c = \frac{16}{3} - \frac{5}{2}
   $$

4. **Find a common denominator (which is 6) and subtract:**
   $$
   c = \frac{32}{6} - \frac{15}{6} = \frac{17}{6}
   $$

5. **Convert back to a mixed number:**
   $$
   c = 2 \frac{5}{6} \text{ cups}
   $$

**Conclusion:**
Alex needs an additional $$ 2 \frac{5}{6} $$ cups of ginger ale to have enough for her punch.

**Answer:** Option **D**. $$ 2 \frac{1}{2} + c = 5 \frac{1}{3} $$
Alex needs $$ 2 \frac{5}{6} $$ more cups of ginger ale. The correct equation is D: $$ 2 \frac{1}{2} + c = 5 \frac{1}{3} $$.

Alex needs cups of ginger ale to make punch for a group of her friends. She has only 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.
B. c
C.
D.
View an example Video Get more help -

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Alex needs cups of ginger ale to make punch for a group of her friends. She has only 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. B. c C. D. View an example Video Get more help -