Let's analyze the problem step by step:
1. Determine the Amount of Paint per Batch:
- Joseph uses 11.2 mL of red paint per batch.
- He also uses 5.6 mL of yellow paint per batch.
- To find out the total amount of paint in one batch, we add the amounts of red and yellow paint:
[tex]\[
\text{Total paint per batch} = 11.2 \, \text{mL} + 5.6 \, \text{mL} = 16.8 \, \text{mL}
\][/tex]
2. Calculate the Number of Batches Needed:
- He needs at least 50 mL of paint in total.
- To figure out how many batches are required, we divide the total amount of paint needed by the amount of paint per batch:
[tex]\[
\text{Batches needed} = \frac{50 \, \text{mL}}{16.8 \, \text{mL per batch}}
\][/tex]
3. Performing the Division:
- Doing the division will give us:
[tex]\[
\frac{50}{16.8} \approx 2.976
\][/tex]
4. Rounding Up to the Nearest Whole Number:
- Since Joseph can't mix a fraction of a batch, he will need to round up to the nearest whole number. Therefore, he needs:
[tex]\[
\lceil 2.976 \rceil = 3
\][/tex]
Thus, Joseph should mix 3 batches of paint to ensure he has at least 50 mL of paint.
