Question

as the buncombe county schools sign language interpreter, kiran, gets paid the following: - $35.50 for every parent - teacher conference that he attends, and - $42 per school - related assembly that he attends as an interpreter. if kiran earns $991 for 27 paid events, how many parent - teacher conferences and how many school - related assemblies did he attend? 10. write a system of equations for this situation where x is the number of parent - teacher conferences and y is the number of assemblies. equation 1: \boxed{} equation 2: \boxed{}

Explanation:

Step1: Define total events equation

Let $x$ = number of parent-teacher conferences, $y$ = number of school assemblies. Total events = 27.
$x + y = 27$

Step2: Define total earnings equation

Earnings from conferences: $35.50x$, earnings from assemblies: $42y$. Total earnings = $991$.
$35.50x + 42y = 991$

Step3: Solve for $x$ from Step1

Rearrange total events equation to isolate $x$.
$x = 27 - y$

Step4: Substitute $x$ into earnings equation

Replace $x$ in the second equation with $27-y$.
$35.50(27 - y) + 42y = 991$

Step5: Expand and simplify the equation

Calculate the product and combine like terms.
$958.5 - 35.50y + 42y = 991$
$6.5y = 991 - 958.5$
$6.5y = 32.5$

Step6: Solve for $y$

Divide both sides by 6.5 to find $y$.
$y = \frac{32.5}{6.5} = 5$

Step7: Solve for $x$

Substitute $y=5$ back into $x=27-y$.
$x = 27 - 5 = 22$

Answer:

System of Equations:

Equation 1: $x + y = 27$
Equation 2: $35.50x + 42y = 991$

Final Counts:

Kiran attended 22 parent-teacher conferences and 5 school-related assemblies.