Question
Marco bought a bag of parsnips that weighed 3 5/6 pounds. He also bought a bag of turnips that weighed 4 1/2 times as much as the parsnips. How many pounds of turnips did Marco buy?
Write your answer as a fraction or as a whole or mixed number.
Write your answer as a fraction or as a whole or mixed number.
Answers
GPT-4o mini
To determine how many pounds of turnips Marco bought, we first need to calculate the total weight of the turnips based on the weight of the parsnips.
1. **Weight of the Parsnips**:
The weight of the parsnips is given as \(3 \frac{5}{6}\) pounds.
To convert this mixed number into an improper fraction, we start by converting \(3\) to sixths:
\[
3 = \frac{3 \times 6}{6} = \frac{18}{6}.
\]
Now, add \(\frac{5}{6}\):
\[
3 \frac{5}{6} = \frac{18}{6} + \frac{5}{6} = \frac{23}{6}.
\]
2. **Weight of the Turnips**:
It is stated that the turnips weigh \(4 \frac{1}{2}\) times as much as the parsnips.
First, we convert \(4 \frac{1}{2}\) into an improper fraction:
\[
4 = \frac{4 \times 2}{2} = \frac{8}{2}.
\]
Adding \(\frac{1}{2}\):
\[
4 \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}.
\]
The weight of the turnips can now be calculated as:
\[
\text{Weight of turnips} = \frac{9}{2} \times \frac{23}{6}.
\]
3. **Multiplying the Fractions**:
We multiply the numerators and the denominators:
\[
= \frac{9 \times 23}{2 \times 6} = \frac{207}{12}.
\]
4. **Simplifying the Fraction**:
Now we can simplify \(\frac{207}{12}\). First, we calculate the greatest common divisor (GCD) of 207 and 12. The factors of 12 are 1, 2, 3, 4, 6, 12.
Checking divisibility:
- \(207 \div 3 = 69\) and \(12 \div 3 = 4\).
We can simplify the fraction by dividing both the numerator and denominator by 3:
\[
\frac{207 \div 3}{12 \div 3} = \frac{69}{4}.
\]
5. **Converting to Mixed Number**:
We can convert \(\frac{69}{4}\) into a mixed number. Dividing \(69\) by \(4\):
- \(69 \div 4 = 17\) remainder \(1\).
Thus,
\[
\frac{69}{4} = 17 \frac{1}{4}.
\]
So, the final weight of the turnips that Marco bought is
\[
\boxed{17 \frac{1}{4}} \text{ pounds.}
\]
1. **Weight of the Parsnips**:
The weight of the parsnips is given as \(3 \frac{5}{6}\) pounds.
To convert this mixed number into an improper fraction, we start by converting \(3\) to sixths:
\[
3 = \frac{3 \times 6}{6} = \frac{18}{6}.
\]
Now, add \(\frac{5}{6}\):
\[
3 \frac{5}{6} = \frac{18}{6} + \frac{5}{6} = \frac{23}{6}.
\]
2. **Weight of the Turnips**:
It is stated that the turnips weigh \(4 \frac{1}{2}\) times as much as the parsnips.
First, we convert \(4 \frac{1}{2}\) into an improper fraction:
\[
4 = \frac{4 \times 2}{2} = \frac{8}{2}.
\]
Adding \(\frac{1}{2}\):
\[
4 \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}.
\]
The weight of the turnips can now be calculated as:
\[
\text{Weight of turnips} = \frac{9}{2} \times \frac{23}{6}.
\]
3. **Multiplying the Fractions**:
We multiply the numerators and the denominators:
\[
= \frac{9 \times 23}{2 \times 6} = \frac{207}{12}.
\]
4. **Simplifying the Fraction**:
Now we can simplify \(\frac{207}{12}\). First, we calculate the greatest common divisor (GCD) of 207 and 12. The factors of 12 are 1, 2, 3, 4, 6, 12.
Checking divisibility:
- \(207 \div 3 = 69\) and \(12 \div 3 = 4\).
We can simplify the fraction by dividing both the numerator and denominator by 3:
\[
\frac{207 \div 3}{12 \div 3} = \frac{69}{4}.
\]
5. **Converting to Mixed Number**:
We can convert \(\frac{69}{4}\) into a mixed number. Dividing \(69\) by \(4\):
- \(69 \div 4 = 17\) remainder \(1\).
Thus,
\[
\frac{69}{4} = 17 \frac{1}{4}.
\]
So, the final weight of the turnips that Marco bought is
\[
\boxed{17 \frac{1}{4}} \text{ pounds.}
\]