Question

the restaurant allows you to design your own meal by selecting one item from each of 5 proteins, 4 vegetables, and 3 sides.
alana does not like fish (protein) or cauliflower (vegetable). what percentage of the dinner options could alana order?
a 36%
b 60%
c 12%
d 5%

Explanation:

Step1: Calculate total meal options

To find the total number of meal options without any restrictions, we use the multiplication principle. The number of proteins is 5, vegetables is 4, and sides is 3. So total options = \(5\times4\times3 = 60\).

Step2: Calculate Alana's meal options

Alana doesn't like fish (so proteins available = \(5 - 1=4\)) and doesn't like cauliflower (so vegetables available = \(4 - 1 = 3\)). The number of sides remains 3. So her options = \(4\times3\times3=36\).

Step3: Calculate the percentage

To find the percentage, we use the formula \(\text{Percentage}=\frac{\text{Alana's options}}{\text{Total options}}\times100\). Substituting the values, we get \(\frac{36}{60}\times100 = 60\%\)? Wait, no, wait. Wait, 433 is 36? Wait 4 proteins, 3 vegetables, 3 sides: 433=36. Total is 543=60. Then 36/60=0.6? Wait no, 36 divided by 60 is 0.6? Wait 36/60 = 0.6, which is 60%? But wait, let me check again. Wait, proteins: 5 total, minus 1 (fish) so 4. Vegetables: 4 total, minus 1 (cauliflower) so 3. Sides: 3. So 433=36. Total: 543=60. Then 36/60 = 0.6, which is 60%? But the option B is 60%. Wait, but let me check the calculation again. Wait 4 (proteins) 3 (vegetables) 3 (sides) = 36. Total is 543=60. Then 36/60 = 0.6, so 60%. So the correct answer is 60%, which is option B. Wait, but wait, maybe I made a mistake. Wait 5 proteins, 4 vegetables, 3 sides: 543=60. Alana: 4 proteins (excluding fish), 3 vegetables (excluding cauliflower), 3 sides. So 433=36. Then 36/60=0.6, which is 60%. So the percentage is 60%.

Answer:

B. 60%