Question

Nola was selling tickets for high school basketball. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said, I wonder whether the dollar belongs inside the cash box or not. The price of tickets for the basketball game was for $3 (for students) or $5 (for adults). She looked inside the cash box and found $209 and ticket stubs for the 47 people in attendance.

Answer 1

The dollar does not belongs to cash box.

Explanation:

Given:

Total money in the cash box = $209

Total number of people = 47

We need to find that the dollar lying on the floor belongs to cash box or not.

Solution,

Let the number of students attending the basketball game be 's'.

And also let the number of adults be 'a'.

So the total number of people is equal to the sum of number of students and number of adults.

framing in equation form, we get;

`s+a=47\ \ \ \ \ equation\ 1`

Again, total money in the cash box is equal to the sum of number of students multiplied with price of each ticket and number of adults multiplied with price of each ticket.

framing in equation form, we get;

`3s+5a=209\ \ \ \ \ equation\ 2`

Now multiplying equation 1 by '3', we get;

`3(s+a)=47*3\\\\3s+3a=141\ \ \ \ equation\ 3`

Now subtracting equation 3 from equation 2, we get;

`(3s+5a)-(3s+3a)=209-141\\\\3s+5a-3s-3a=68\\\\2a=68`

Now using division property we will divide both side by '2' and get;

`(2a)/(2)=(68)/(2)\\\\a=34`

On substituting the value of 'a' in equation 1 we get;

`s+34=47\\`

Now using subtraction property we will subtract both side by '34' and get;

`s+34-34=47-34\\\\s=13`

Here we get the whole value for number of students and number of adults.

That means the dollar does not belongs to cash box.