The revenue in dollars from a school play is given by the expression 5x+2y, where x is the of adult tickets sold and y is the number of student tickets sold. If the revenue is $220, find the x- and y- intercepts and explain what they represent in the context of the problem.
To find the x-intercept, we set y = 0 and solve for x. Similarly, to find the y-intercept, we set x = 0 and solve for y.
1. x-intercept:
Setting y = 0 in the given expression, we get:
5x + 2(0) = 220
5x = 220
Dividing both sides by 5:
x = 44
Therefore, the x-intercept is (44, 0).
In the context of the problem, the x-intercept represents the number of adult tickets sold (x) when no student tickets (y) are sold. Since there are no student tickets sold, the revenue solely comes from the adult tickets.
2. y-intercept:
Setting x = 0 in the given expression, we get:
5(0) + 2y = 220
2y = 220
Dividing both sides by 2:
y = 110
Therefore, the y-intercept is (0, 110).
In the context of the problem, the y-intercept represents the number of student tickets sold (y) when no adult tickets (x) are sold. Since there are no adult tickets sold, the revenue solely comes from the student tickets.
To summarize:
- The x-intercept (44, 0) represents the number of adult tickets sold when no student tickets are sold.
- The y-intercept (0, 110) represents the number of student tickets sold when no adult tickets are sold.
5x+2y according to your definition of x and y shows me that each adult ticket costs $5 and a student's ticket costs $2.
for 5x + 2y = 220
the x-intercept is 44 , the y=0
the y-intercept is 110, the x = 0
Meaning:
if no students show up, then the number of adult that went to the play is 44
if not adults show up, then the number of students at the play was 110