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.

The dollar does not belongs to cash box.

Step-by-step 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;

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;

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

Now subtracting equation 3 from equation 2, we get;

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

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

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

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

That means the dollar does not belongs to cash box.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .