Step-by-step explanation:
Let x be number of seniors and y be number of juniors going to attend dance.
The dance hall can hold 560 students. We can represent this information as: [tex]x+y\leq 560...(1)[/tex]
We have been given that tickets for the dance are sold for $5 to seniors and $7 to juniors. So the amount raised after selling tickets to seniors will be 5x and the amount raised after selling tickets to juniors will be 7y.
We need to raise at least $3500 by selling both types of tickets.
We can represent this information as: [tex]5x+7y\geq 3500...(2)[/tex]
Therefore, our desired system of inequalities will be:
[tex]x+y\leq 560...(1)[/tex]
[tex]5x+7y\geq 3500...(2)[/tex]
we can define the variables:
x = number of senior tickets sold
y = number of junior tickets sold.
Then with the given information we can write:
x + y = 560
x*$5 + y*$7 = $3500
This is the system of equations that models this situation.
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