To determine how many pints of paint Henry will need altogether while maintaining the same shade of orange, we need to establish the ratio of red to yellow paint he initially used.
From the problem, we know that:
- He initially used 2 pints of red paint and 3 pints of yellow paint.
This gives us a ratio of red to yellow of:
\[ \frac{\text{red}}{\text{yellow}} = \frac{2}{3} \]
Now, if Henry uses 9 pints of yellow paint and wants to maintain the same ratio of red to yellow, we can calculate how much red paint he will need.
Let \( R \) be the amount of red paint needed when he uses 9 pints of yellow paint. Using the ratio:
\[ \frac{R}{9} = \frac{2}{3} \]
To find \( R \), we can cross-multiply:
\[ R \cdot 3 = 2 \cdot 9 \] \[ 3R = 18 \] \[ R = \frac{18}{3} = 6 \]
So, Henry will need 6 pints of red paint.
Now, we can find the total amount of paint he will need:
- Yellow paint: 9 pints
- Red paint: 6 pints
Adding them together gives:
\[ \text{Total paint} = 9 + 6 = 15 \text{ pints} \]
Therefore, Henry will need 15 pints of paint altogether to achieve the same shade of orange.