Students at a Brennan volleyball game sell tickets for their crowd. The tickets cost $5 per adult and $3 per student. At the end of the night, they saw that they had made $840 but they did not remember to calculate how many of each type of ticket they sold. They did find that they gave out 224 tickets. Help them find out many of each type of ticket they sold, both adult and student tickets.

 

Number of tickets sold to adults = 84 , and,

Number of tickets sold to students = 140

Step-by-step explanation

Let the number of adult tickets = x ,

and, the number of student tickets = y

Now, cost of adult ticket = $5 and cost of student ticket = $3

??? Total money made with adult tickets = 5x and total money made with student tickets = 3y

??? Total money made with adult and student tickets combined = 5x + 3y

??? 840 = 5x + 3y .....eq1?? {??? Total money made with tickets=$840}

Now, total tickets sold = 224

??? x + y = 224 ......eq2?? {??? Total tickets=Tickets sold to adults + Tickets sold to students}

Now, multiplying eq2 with 3 on both sides, we get,

3(x+y) = 3(224)

??? 3x + 3y = 672 .....eq3

Now, subtracting eq3 from eq1, we get,

(5x+3y) - (3x+3y) = 840 - 672

??? 2x = 168

??? x = 84

Putting x=84 in eq2, we get,

84 + y = 224

??? y = 140

Therefore,

Number of tickets sold to adults = x = 84 , and,

Number of tickets sold to students = y = 140