To find out how many cases of soda Philip can purchase while staying under his budget, we need to set up an inequality based on the information provided.
Philip's budget is $496, and he has already spent $400. Therefore, the remaining amount he can spend is:
\[ 496 - 400 = 96 \]
Each case of soda costs $8. Let \( x \) be the number of cases of soda he can purchase. The cost for \( x \) cases of soda would be \( 8x \).
Now, we can set up the inequality:
\[ 8x < 96 \]
Next, we solve for \( x \):
\[ x < \frac{96}{8} \] \[ x < 12 \]
This means Philip can purchase up to 11 cases of soda (since \( x \) must be a whole number and it needs to be less than 12).
Now, let's look at the options given and find the largest number less than or equal to 11 in the ranges:
- Option A: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
- Option B: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
- Option C: 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
- Option D: 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
The largest number of cases of soda Philip can purchase is 11. This number appears in options A and B.
So, the correct answer is both Option A and B.