Martin decided to buy 2 bags of grapes weighing $$ 5 \frac{2}{3} $$ pounds each, instead of the 3 bags weighing $$ 4 \frac{1}{5} $$ pounds each, because the bigger bags were on sale. Did he end up with more grapes or less grapes by buying the bigger bags? He ended up with about One-half pound less grapes. He ended up with about One-half pound more grapes. He ended up with about 1 pound more grapes. He ended up with about 1 pound less grapes.

Question

UpStudy AI · Accepted Answer

To determine whether Martin ended up with more or less grapes by buying the bigger bags, we need to calculate the total weight of grapes he would have gotten from both options.

1. **Calculating the weight of the 2 bags of grapes weighing $$ 5 \frac{2}{3} $$ pounds each:**

First, convert $$ 5 \frac{2}{3} $$ to an improper fraction:
   $$
   5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3} \text{ pounds}
   $$

Now, calculate the total weight for 2 bags:
   $$
   2 \times \frac{17}{3} = \frac{34}{3} \text{ pounds}
   $$

2. **Calculating the weight of the 3 bags of grapes weighing $$ 4 \frac{1}{5} $$ pounds each:**

First, convert $$ 4 \frac{1}{5} $$ to an improper fraction:
   $$
   4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \text{ pounds}
   $$

Now, calculate the total weight for 3 bags:
   $$
   3 \times \frac{21}{5} = \frac{63}{5} \text{ pounds}
   $$

3. **Finding a common denominator to compare the two weights:**

The least common multiple of 3 and 5 is 15. We will convert both fractions to have a denominator of 15.

For $$ \frac{34}{3} $$:
   $$
   \frac{34}{3} = \frac{34 \times 5}{3 \times 5} = \frac{170}{15}
   $$

For $$ \frac{63}{5} $$:
   $$
   \frac{63}{5} = \frac{63 \times 3}{5 \times 3} = \frac{189}{15}
   $$

4. **Comparing the two weights:**

Now we can compare $$ \frac{170}{15} $$ and $$ \frac{189}{15} $$:
   $$
   \frac{170}{15} < \frac{189}{15}
   $$

This means that Martin ended up with less grapes by buying the bigger bags.

5. **Calculating the difference:**
   $$
   \frac{189}{15} - \frac{170}{15} = \frac{19}{15} \text{ pounds}
   $$

Converting $$ \frac{19}{15} $$ to a mixed number:
   $$
   \frac{19}{15} = 1 \frac{4}{15} \text{ pounds}
   $$

Thus, Martin ended up with about 1 pound less grapes by buying the bigger bags.

The correct answer is:
**He ended up with about 1 pound less grapes.**
He ended up with about 1 pound less grapes.

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions