20% of the sandwiches in a restaurant had fish. 1/4 had cheese and the remaining 77 had vegetables.

a) what decimal fraction of the sandwiches had vegetables?

b) How many sandwiches were in the restaurant?

c) How many more cheese sandwiches than fish sandwiches were in the restaurant?

0.2x + 0.25x + 77 = x

77 = 0.55x

77/0.55 = x

140 = x total sandwiches

77/140 = ________ sandwiches with vegetables

What is your answer for c?

55.45

a) To find the decimal fraction of sandwiches that had vegetables, we need to calculate the proportion of sandwiches with vegetables out of the total number of sandwiches. We know that 20% of the sandwiches had fish, 1/4 had cheese, and the remaining 77 had vegetables.

The proportion of sandwiches with vegetables is calculated by subtracting the percentages of fish and cheese sandwiches from 100%. So, the proportion of vegetable sandwiches is:

100% - 20% (fish) - 25% (cheese) = 55%

Therefore, the decimal fraction of sandwiches that had vegetables is 0.55.

b) To determine the total number of sandwiches in the restaurant, we need to sum up the number of sandwiches with fish, cheese, and vegetables. We are given that 20% of the sandwiches had fish, 1/4 had cheese, and the remaining 77 had vegetables.

Let's assume the total number of sandwiches is represented by "x." We can set up the following equation:

0.20x (fish) + (1/4)x (cheese) + 77 (vegetables) = x

Simplifying the equation:

0.20x + 0.25x + 77 = x

Combining like terms:

0.45x + 77 = x

Now, we can isolate the variable:

0.55x = 77

Dividing both sides by 0.55:

x = 77 / 0.55

x ≈ 140

Therefore, there were approximately 140 sandwiches in the restaurant.

c) To find the difference between the number of cheese sandwiches and fish sandwiches, we need to subtract the number of fish sandwiches from the number of cheese sandwiches.

Given that 20% of the sandwiches had fish and 1/4 had cheese, we can calculate the number of cheese sandwiches and fish sandwiches using the total number of sandwiches:

Fish sandwiches = 0.20 * Total number of sandwiches
Cheese sandwiches = (1/4) * Total number of sandwiches

Let's substitute the total number of sandwiches we found previously:

Fish sandwiches ≈ 0.20 * 140
Cheese sandwiches ≈ (1/4) * 140

Fish sandwiches ≈ 28
Cheese sandwiches ≈ 35

To find the difference, we subtract the number of fish sandwiches from the number of cheese sandwiches:

Cheese sandwiches - Fish sandwiches = 35 - 28 = 7

Therefore, there were 7 more cheese sandwiches than fish sandwiches in the restaurant.