Question

1. school dance the sign below indicates the cost of attending the big dance. in all, $320 was made. this can be represented by the function 2x + 5y = 320. find the x - and y - intercepts. what do they represent? dance ticket prices fr/soph. $2 jr/sr. $5

Explanation:

Step1: Find the x - intercept

Set \(y = 0\) in the equation \(2x+5y = 320\).
Substitute \(y = 0\) into \(2x+5y=320\), we get \(2x+5\times0 = 320\), which simplifies to \(2x=320\).
Solve for \(x\): \(x=\frac{320}{2}=160\).
The x - intercept is \((160,0)\). It represents the number of Fr/Soph tickets sold if no Jr/Sr tickets were sold.

Step2: Find the y - intercept

Set \(x = 0\) in the equation \(2x + 5y=320\).
Substitute \(x = 0\) into \(2x+5y = 320\), we get \(2\times0+5y=320\), which simplifies to \(5y=320\).
Solve for \(y\): \(y=\frac{320}{5}=64\).
The y - intercept is \((0,64)\). It represents the number of Jr/Sr tickets sold if no Fr/Soph tickets were sold.

Answer:

The x - intercept is \(160\) (when \(y = 0\), it means 160 Fr/Soph tickets sold with 0 Jr/Sr tickets sold). The y - intercept is \(64\) (when \(x = 0\), it means 64 Jr/Sr tickets sold with 0 Fr/Soph tickets sold).