Question

If 146 people attend a concert and tickets for adults cost $3 while tickets for children cost $1.75 and total receipts for the concert was $355.5, how many of each went to the concert?

Answer 1

80 adults and 66 children attended the concert

Explanation:

Two equations are needed to solve this problem

1. One equation focusing on the number of people who attended
2. One equation focusing on the costs of tickets

Let x be the number of adults and let y be the number of children

For equation 1:

The number of adults plus the number of children that attended is the total

x+y=146

For equation 2:

Since the cost of an adult's ticket is $3, multiply that by the number of adults

Do the same for children, multiply the price of a child's ticket by the number of children that attended

Add them together and they should equal the total profit

3x+1.75y= 355.5

Now rearrange equation 1, isolate for either x or y

y= 146-x

Substitute the rearranged equation back in for the isolated variable in equation 2

3x+1.75y= 355.5

3x+ 1.75(146-x)= 355.5

Now simplify the equation

3x+ 255.5- 1.75x= 355.5

Rearrange the equation so that the variables are on one side and the numbers are on the other

3x- 1.75x= 355.5- 255.5

1.25x= 100

Isolate for x

x= 100/1.25

x=80

Recall x was the number of adults that attended so,

80 adults attended the concert

Now, substitute this value back into either equation 1 or 2

To keep things simple, let's use equation 1

x+y= 146

y= 146-80

y= 66

Recall y was the number of children, so

66 children attended the concert

To verify, substitute those values back into equation 2,

3x+1.75y = 355.5

($3*80 adults) + ($1.75*66 children)= $355.50

$240+ $115.50= $355.50

$355.50 = $355.50