There are 40 students in Joan's class. She plans to invite them to her birthday party. She asked them to suggest a theme for her party. Three of every 8 students suggested a rainbow-themed party. How many suggested a rainbow themed party. How many did not?

To find out how many students suggested a rainbow-themed party, we can first calculate the number of students who suggested this theme based on the ratio given (3 of every 8 students).

1. Calculate the number of students who suggested a rainbow-themed party: \[ \text{Number of students suggesting a rainbow theme} = \left( \frac{3}{8} \right) \times 40 \] \[ = \frac{3 \times 40}{8} = \frac{120}{8} = 15 \]

2. Calculate the number of students who did not suggest a rainbow-themed party: \[ \text{Number of students not suggesting a rainbow theme} = 40 - 15 = 25 \]

Thus, 15 students suggested a rainbow-themed party, and 25 students did not.