Question
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\begin{tabular}{l} Determine if the rates 8 \\ cups with 56 forks and 4 \\ cups with 28 forks are \\ equivalent. Justify your \\ answer. \\ \\ \\ \hline\end{tabular}

Ask by Salinas Gough. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Both rates are equivalent because they both equal 7 forks per cup.

Solution

1. Calculate the ratio for 8 cups with 56 forks: - \[ \frac{56 \text{ forks}}{8 \text{ cups}} = 7 \text{ forks per cup} \] 2. Calculate the ratio for 4 cups with 28 forks: - \[ \frac{28 \text{ forks}}{4 \text{ cups}} = 7 \text{ forks per cup} \] 3. Since both rates result in \(7\) forks per cup, the rates are equivalent.

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Beyond the Answer

To determine if the rates are equivalent, we can simplify each rate. For the first rate, we have 8 cups with 56 forks. Dividing both numbers by 8 yields 1 cup with 7 forks. For the second rate, we have 4 cups with 28 forks. Dividing both numbers by 4 gives us 1 cup with 7 forks as well. Since both rates simplify to 1 cup with 7 forks, we can conclude that the rates are indeed equivalent. In essence, whether you're serving up a cup of cereal or laying out the forks for a fancy dinner, having equivalent rates simplifies your tasks and ensures you get it just right. Keeping things in balance—like cups and forks or ingredients and quantities—helps avoid hiccups in any meal prep or party planning!

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