Question

If 107 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $3.5 and total receipts for the concert was $391.25, how many of each went to the concert?

Answer 1

Explanation:

Let's assume that 'a' adults and 'c' children attended the concert.

From the problem statement, we know that:

a + c = 107 ---(1) (The total number of people who attended the concert is 107)

3.75a + 3.5c = 391.25 ---(2) (The total revenue generated from the concert is $391.25)

Now, we need to solve these two simultaneous equations to find the values of 'a' and 'c'.

To do this, we can use the elimination method to solve these equations.

First, we will multiply equation (1) by 3.5 to eliminate 'c':

3.5a + 3.5c = 374.5 ---(3)

Next, we will subtract equation (3) from equation (2):

3.75a + 3.5c - (3.5a + 3.5c) = 391.25 - 374.5

0.25a = 16.75

a = 67

Now that we know the value of 'a', we can substitute it into either equation (1) or (2) to find the value of 'c':

a + c = 107

67 + c = 107

c = 40

Therefore, there were 67 adults and 40 children at the concert.