Let's start by determining the initial number of crates, the number of crates removed (rotten, sold, and canned), and finally the number of crates left.
1. Initial Crates of Tomatoes:
The problem states that there were initially [tex]\(\frac{97}{4}\)[/tex] crates of tomatoes in the barn.
[tex]\[
\text{Initial crates} = \frac{97}{4} = 24.25
\][/tex]
2. Crates of Tomatoes Rotten:
Out of the initial crates, [tex]\(\frac{38}{5}\)[/tex] crates were rotten and had to be thrown out.
[tex]\[
\text{Crates rotten} = \frac{38}{5} = 7.6
\][/tex]
3. Crates of Tomatoes Sold:
Joe sold [tex]\(\frac{25}{3}\)[/tex] crates of tomatoes.
[tex]\[
\text{Crates sold} = \frac{25}{3} = 8.333333333333334
\][/tex]
4. Crates of Tomatoes Canned:
Joe also canned [tex]\(\frac{47}{6}\)[/tex] crates of tomatoes.
[tex]\[
\text{Crates canned} = \frac{47}{6} = 7.833333333333333
\][/tex]
5. Total Crates Removed:
To find the total number of crates removed (rotten, sold, and canned), we sum the individual quantities:
[tex]\[
\text{Total crates removed} = 7.6 + 8.333333333333334 + 7.833333333333333 = 23.766666666666666
\][/tex]
6. Crates Left:
We now subtract the total crates removed from the initial number of crates to find the number of crates left:
[tex]\[
\text{Crates left} = 24.25 - 23.766666666666666 = 0.4833333333333343
\][/tex]
Therefore, the number of crates of tomatoes left in the barn is approximately [tex]\(0.483\)[/tex] crates.
