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Ciarra and Ashley sold tickets for the high school basketball tournament. For the opening game of the tournament, girls sold 20 students tickets and 30 non-students tickets and made $190. For the championship game, they sold 50 students tickets and 40 non-students tickets and made $300. What was the price of a student ticket? What was the price of a non-student ticket?

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arokoyuola

Answer:

a = $2, b = $5

Step-by-step explanation:

We begin by converting the two scenarios into simultaneos linear equations.

let a = student tickets and b = non-student tickets

20a + 30b = $190

50a + 40b = $300

from equation 1, 20a + 30b = 190

a = 190/20 - 30b/20

a = 9.5 - 1.5b

Substituting this into equation 2,

50(9.5 - 1.5b) + 40b = 300

475 - 75b + 40b = 300

475 - 35b = 300

-35b = 300 - 475

-35b = -175

b = 175/35

b = $5

Now we proceed to put the value of b into equation 1;

20a + 30b = $190

20a + 30($5) = $190

20a + $150 = $190

20a = $190 - $150

20a = 40

a = $2

Step-by-step explanation:

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