The table shows the number of shirts a football club ordered, but one of the frequencies is missing.

The football club ordered a total of 57 blue shirts. How many medium blue shirts did the football club order?

\begin{tabular}{|c|c|c|c|c|}
\hline
\multicolumn{2}{|c}{} & \multicolumn{3}{c|}{Colour} \\
\cline {2-5}
& Red & Blue & Yellow \\
\hline
\multirow{3}{*}{Size} & Small & 11 & 18 & 20 \\
\cline {2-5}
& Medium & 30 & & 5 \\
\cline {2-5}
& Large & 5 & 25 & 2 \\
\hline
\end{tabular}



Answer :

To determine how many medium blue shirts the football club ordered, we'll follow these steps:

1. Identify given values:
- The total number of blue shirts ordered is 57.
- The number of small blue shirts ordered is 18.
- The number of large blue shirts ordered is 25.
- The number of medium blue shirts ordered is missing and needs to be found.

2. Set up the equation:
- The total number of blue shirts (57) is the sum of small, medium, and large blue shirts.
- Using the known quantities, our equation will be:
[tex]\[ \text{Total blue shirts} = \text{Small blue shirts} + \text{Medium blue shirts} + \text{Large blue shirts} \][/tex]
- Substitute the given values into the equation:
[tex]\[ 57 = 18 + \text{Medium blue shirts} + 25 \][/tex]

3. Simplify the equation:
- Combine the number of small and large blue shirts:
[tex]\[ 57 = 18 + 25 + \text{Medium blue shirts} \][/tex]
[tex]\[ 57 = 43 + \text{Medium blue shirts} \][/tex]

4. Solve for the number of medium blue shirts:
- Isolate the variable ([tex]\(\text{Medium blue shirts}\)[/tex]) by subtracting 43 from both sides of the equation:
[tex]\[ 57 - 43 = \text{Medium blue shirts} \][/tex]
[tex]\[ 14 = \text{Medium blue shirts} \][/tex]

Thus, the football club ordered 14 medium blue shirts.