Concert attendants problem

Question

If 101 people attend a concert and tickets for adults cost $4 while tickets for children cost $2.5 and total receipts for the concert was $320, how many of each went to the concert?

Answer 1

A + C = 101

4A + 2.5C = 320

2.5A + 2.5C = 2.5(101) = 252.5

1.5A = 320-252.5 = 67.5

A = 67.5/1.5 = 45 adults

C = 101-45 = 56 children

4(45) + 2.5(56) = 180 + 140 = 320

Answer 2

If 101 people attend a concert and tickets for adults cost $4 while tickets for children cost $2.5 and total receipts for the concert was $320, how many of each went to the concert?

Let's have x represent the number of adults and y represent the number of children.

We know the total number of attendees is 101 but we don't know how many adults or how many children came.

So: x+y=101

We know the total money made was $320 We also know the cost of one adult ticket and 1 child ticket.

so: 4x+2.5y+320

Now we have a system of equations:

x+y=101

4x+2.5y=320

We can solve this system by elimination. Let's eliminate the x variable. To do this, multiply the first equation by -4.

So you would have:

-4x-4y=-404

4x+2.5y=320

-1.5y=-84 Now, divide both sides by -1.5 and you get y=56

Put this answer into the top equation and solve that for x. Then you will have both your answers. Good luck!