Question

A soccer team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $6, deluxe for $4, and regular for $2. The total number of tickets sold was 273, and the total amount of money from raffle tickets was $836. If 118 more regular tickets were sold than deluxe tickets, how many premium tickets were sold?

Answer 1

Step-by-step explanation

We get three linear equations from the information given, where

p= number of premium tickets

d = number of deluxe tickets

r = number of regular tickets:

`\left \{ {{p+d+r=273} \atop \\{6p+4d+2r=836} \right.`

and the applying third r=118+d, we get

`\left \{ {p+d+118+d=273} \atop {6p+4d+2d+236=836}} \right.`

`\left \{ {{p+2d=115} \atop {6p+6d=600}} \right.`

Now we get from the upper one

p=115-2d

solving the another equation gives us

6*115-12d+6d=600,

hence d=15

and by replacing

p=115-2*15=85.

85 premium tickets were sold

Answer 2

45 premium tickets were sold

Explanation:

p = premium

d = deluxe

r = regular

p+d+r = 273

6p+4d + 2r = 836

118+d = r

Replace r with 118+d

p+d+118+d = 273

p +2d = 273-118

p+2d = 155

6p+4d + 2(118+d) = 836

6p+4d + 236+2d = 836

6p +6d = 836-236

6p + 6d = 600

Divide by 6

p+d = 100

d = 100-p

Replace d in p +2d= 155

p +2(100-p) = 155

p+200-2p = 155

-p = 155-200

-p =-45

p =45

45 premium tickets were sold