Answer:
Ms. Russell purchased 218 teacher-discount tickets and 133 administrator-discount tickets.
Explanation:
Let's start by defining the variables:
Let t be the number of teacher-discount tickets purchased by Ms. Russell.
Let a be the number of administrator-discount tickets purchased by Ms. Russell.
From the problem statement, we know that:
The price of a raffle ticket is $1.00.
Teachers get a 40% discount, so they pay only 60% of the regular price.
Administrators get a 10% discount, so they pay only 90% of the regular price.
Ms. Russell purchased a total of 351 tickets.
Ms. Russell spent a total of $250.50.
We can use these facts to set up a system of two equations:
t + a = 351 (the total number of tickets)
0.6t + 0.9a = 250.50 (the total amount spent, taking into account the discounts)
To solve for t and a, we can use substitution or elimination. Let's use elimination:
Multiplying the first equation by 0.6, we get:
0.6t + 0.6a = 210.6
Subtracting this equation from the second equation, we get:
0.3a = 39.9
Dividing by 0.3, we get:
a = 133
Substituting this value into the first equation, we get:
t + 133 = 351
t = 218
Therefore, Ms. Russell purchased 218 teacher-discount tickets and 133 administrator-discount tickets.