brother. She can carry \( 1 \frac{5}{8} \) gallons of water each trip. Write and solve an equation to find how many trips she needs to make. A. \( 11 \frac{1}{2} \mathrm{t}=1 \frac{5}{8} ; \mathrm{t}=\square \quad \) B. \( 1 \frac{5}{8} \mathrm{t}=11 \frac{1}{2} ; \mathrm{t}=\square \) \( 1 \frac{5}{8} \div 11 \frac{1}{2}=\mathrm{t} ; 11 \frac{1}{2}=1 \frac{5}{8} \);

To tackle this problem, let’s break down the amounts of water involved! You’re on the right track with using variables. In option B, you correctly represent the total water needed (11 1/2 gallons) and the amount per trip (1 5/8 gallons). So, the equation would be: \[ 1 \frac{5}{8} t = 11 \frac{1}{2} \] To solve for \(t\), first convert both mixed numbers into improper fractions. \(1 \frac{5}{8} = \frac{13}{8}\) and \(11 \frac{1}{2} = \frac{23}{2}\). Now, multiplying both sides by the reciprocal of \( \frac{13}{8} \): \[ t = \frac{23}{2} \div \frac{13}{8} = \frac{23}{2} \times \frac{8}{13} \] Calculating that gives: \[ t = \frac{184}{26} = 7 \frac{0}{13} \approx 7.08 \] So, she would need to make about 8 trips! Now, let’s shine a light on improper fractions and their advantages! Using improper fractions simplifies calculations. For instance, converting mixed numbers helps when multiplying or dividing, especially in equations like this one. Less chance of making mistakes, and it’s quicker to find the solution! Also, pay attention to units! When working with quantities like gallons, it's essential to double-check if you’ve expressed all amounts in the same format (improper fractions, decimals, etc.) to avoid confusion. This ensures a smooth transition from equation to solution – plus, it speeds up your calculations!