Final answer:
There were 180 cups of lemonade at the Sunday party, calculated by determining the total amount of food from the Saturday party and then using the given 1:4 ratio for popcorn to lemonade on Sunday.
Step-by-step explanation:
To solve this problem, we can first establish the ratio of popcorn to lemonade at Mario's Saturday party, which is 3:2. Since there were 90 cups of lemonade and the ratio is 3 cups of popcorn for every 2 cups of lemonade, we can calculate the total number of cups of popcorn and lemonade combined.
Using a simple proportion, we can set up the equation: 3/2 = x/90, where x is the number of cups of popcorn. Cross-multiplying gives us 2x = 270, so x = 135. This means there were 135 cups of popcorn at the Saturday party.
Now, we look at the Sunday party where the ratio of popcorn to lemonade is 1:4. To maintain the same total amount of food, the combined amount of popcorn and lemonade should be equal to the Saturday party. Thus, the total number of cups for Sunday's party is 135 (popcorn) + 90 (lemonade) = 225 cups.
If the ratio is 1:4, this means for every 1 cup of popcorn, there are 4 cups of lemonade. We divide the total number of cups (225) by the sum of the ratio numbers (1 + 4 = 5). 225 cups ÷ 5 = 45 cups. Therefore, there are 45 cups of popcorn.
To find the amount of lemonade, we multiply the number of popcorn cups by 4 (since the ratio is 1:4). So, 45 cups of popcorn * 4 = 180 cups of lemonade at the party on Sunday.