Question

On a trip, the fare was 50¢ for each adult and 25¢ for each child. If 30 passengers paid $12.25, how many adults and children went?

Is this the right way to set up the equation?
50x + 25(30 - x) = 1225

Answer 1

25x + 50x = 30(1225) is the equation that wouldn't work

Explanation:

Given,

Total passenger = 30

There can be only two cases,

Case 1 : Let x be the number of adults,

So, the number of children = 30 - x,

Since, the total fare is $12.25 or 1225¢ ( 1 dollar = 100 cents ) in which 50¢ is for each adult and 25¢ is for each child,

⇒ 50x + 25(30 - x) = 1225,

Case 2 : let x be the number of children,

So, the number of adult = 30 - x,

The equation would be,

⇒ 50(30 - x) + 25x = 1225

Hence, the equations that could not be used to solve the given problem is,

25x + 50x = 30(1225)

Explanation:

Answer 2

Fare for each adult = 0.50 dollars
Fare for each child = 0.25 dollars
Total number of passengers = 30
Total amount paid for the trip = 30 dollars
Lat us assume the number of adults = x
Then
The number of children = 30 - x
So
0.50x + 0.25(30 - x) = 12.25
50x + 25(30 - x) = 1225
This is the right way of setting up the equation and you have done it correctly.