A charity fund-raiser consisted of a spaghetti dinner where a total of 387 people were fed. They charged $6.80 for adults and children were half price. If they took in $2444.60, find out how many adults and how many children attended the dinner. I have no idea how to solve this problem. I would appreciated any help I can get.
n = number of adults
6.80n = value of adults
387 - n = number of children
3.40(387 - n) = value of children
6.80n + 3.40(387 - n) = 2444.60
Solve for n = number of adults
387 - n = number of children
To solve this problem, let's define some variables.
Let's call the number of adults who attended the dinner "A" and the number of children "C".
From the given information, we know that the total number of people who were fed was 387. So, we can write an equation based on this information:
A + C = 387
We also know that the cost for adults was $6.80 and children were half price, so the cost for children is $6.80/2 = $3.40.
The total amount of money taken in was $2444.60, so we can write another equation based on this information:
(6.80 * A) + (3.40 * C) = 2444.60
Now, we have a system of two equations:
A + C = 387
6.80A + 3.40C = 2444.60
To solve these equations, we can use the method of substitution.
Rearrange the first equation to solve for A:
A = 387 - C
Substitute this value of A into the second equation:
6.8 * (387 - C) + 3.4C = 2444.60
Now, solve for C:
2619.60 - 6.8C + 3.4C = 2444.60
-3.4C = -175
C = 175/3.4
C ≈ 51.47
Since the number of people can't be a fraction, we'll round it to the nearest whole number:
C ≈ 51
Now, substitute this value of C back into the first equation to find A:
A + 51 = 387
A = 387 - 51
A = 336
Therefore, 336 adults and 51 children attended the dinner.