Answer:
80 adults and 66 children attended the concert
Step-by-step explanation:
Two equations are needed to solve this problem
- One equation focusing on the number of people who attended
- One equation focusing on the costs of tickets
Let x be the number of adults and let y be the number of children
<u>For equation 1:</u>
The number of adults plus the number of children that attended is the total
x+y=146
<u>For equation 2: </u>
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
