If 87 people attend a concert and tickets for adults cost $3 while tickets for children cost $2 and total receipts for the concert was $208, how many of each went to the concert?

Answer 1

You have 2 unknowns so you need to find 2 equations to solve this.

Let x = number of adults that attended

y = number of children that attended

Eq. I: x + y = 87

Eq. II: 3x + 2y = 208

We can use either the elimination or substitution method to solve this. Let's use the substitution method. Using Eq. I we can rearrange it to find out x is in terms of y:

x + y = 87

x = 87 - y

Using this value for y in Eq. II we can solve for y:

3x + 2y =208

3(87 - y) + 2y =208

261 - 3y + 2y = 208

261 - y = 208

-y = 208 - 261

-y = -53

y = 53

Using this value of y in either Eq. I or II we can solve for x:

Eq. I: x + y = 87

x + 53 = 87

x = 87 - 53

x = 34

Therefore, the number of adults was 34 and the number of children was 53.

Hope this helps!

Answer 2

x + y = 87

3x + 2y = 208

x = 208 - 174 = 34 adults

y = 87 - 34 = 53 children

Answer 3

Lets call adult tickets A and children tickets C, so the amount of money made from adult tickets is 3A and the amount of money made from children tickets 2C, them added together is 208, the total amount of people is 87:

A+C=87, C=87-A

3A+2C=208 lets plug the C into this equation and solve:

3A+2(87-A)=208, 3A+174-2A=208, A=34 now lets plug A back into C:

C=87-34, C=53

34 adults and 53 children attended the concert

Answer 4

A=# of adult tickets and C=# of child tickets

A+C = 87

3A+2C=208

Multiply the first equation by 2 and subtract

A=208-174

You get the solution from here.