The # of student tickets sold was equal to 3 times the # of adult tickets sold decreased by 56. Student tickets cost $3.50 and adults $5.

Question

The total receipts were $2005. How many adult tickets were sold? I don't know how to write the equation for this. Pls help me solve this

Answer 1

Let s = number student tickets sold

Let a = number adult tickets sold

 

s is 56 less than 3 times a:

s = 3a - 56      {equation 1}

 

Total receipts are $2005 with student tickets cost $3.50 and adult tickets cost $5

3.5s + 5a = 2005    {equation 2}

 

Substitute 3a-56 in place of s in equation 2 and solve for a to find # adult tickets

 

3.5(3a-56) + 5a = 2005

10.5a - 196 + 5a = 2005

15.5a = 2005 + 196

15.5a = 2201

 

a = 142 adult tickets sold

 

s = 3(142) - 56 = 370 student tickets sold