How do I set up this question

Question

If 102 people attend a concert and tickets for adults cost $2 while tickets for children cost $1.75 and total receipts for the concert was $195.25, how many of each went to the concert?

Answer 1

Hi, Jenny.

Okay , so let's set some variables.

Let's call the number of adult tickets sold A.

Let's call the number of child tickets sold C

So, if 102 people went to the concert, then A + C = 102

2.00(A ) + 1.75(C) = 195.25

Since we know that there are 102 people altogether, we can say C = 102 - A

Now we can substitute that value for C into the above equation.

2.00(A) + 1.75(102 - A) = 195.25

2.00A + 178.5 - 1.75A = 195.25

.25A = 195.25 - 178.5

.25A = 16.75

A = 67

So 67 adults went to the concert.

C = 102 - 67 = 35

So 35 children went to the concert

Check the answer:

2(67) + 1.75(35) = 134 + 61.25 = 195.25

Therefore, the answers are correct.

Answer 2

I will not solve this problem for you but I will tell you how to do it.

A+C+102 => A = 102-C

2A + 1.75C = 195.25

Substitute

This will now give you a rather messy equation in the unknown C which you should be able to solve.