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?

80 adults and 66 children attended the concert

Step-by-step explanation:

Two equations are needed to solve this problem

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

111

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