i need help with this word problem

Question

A theatre contains 455 seats and the ticket prices for a recent play were $46 for adults and $28 for children. If the total of proceeds were $15,638 for a sold out matinee, how many of each type of ticket were sold?

Answer 1

Let A = number of adult tickets sold.

Let C = number of children tickets sold.

A + C = 455

46A + 28C = 15638

I will solve by substitution and rewrite the 1st equation as C = 455 - A

46A + 28(455 - A) = 15638

46A + 12740 - 28A = 15638

18A = 2898

A = 161

C = 294

161 adult tickets and 294 children tickets were sold.

Answer 2

First look for what we need to find out.

In this question, we need to find how many adult tickets and how many child tickets were sold?

Let's name the unknown variables, Adult tickets sold as 'x' and children's tickets sold as 'y'

Now look for the information given.

Since its a sold-out matinee show, the total number of tickets sold would be equal to the total number of seats.

i.e x+ y = 455 ------------------------------------------------ Equation1

Price for an adult ticket = $46

So, the price for x adult tickets would be 46x

Price for a child ticket = $28

So, the price for y children's tickets would be 28y

Total price for tickets = 46x + 28y = 15,638-----------------------Equation2

Let's solve for x by substituting the value of y from Equation1 in Equation2

i.e y = 455 - x

Our Equation 2 becomes

46x + 28(455 - x) = 15,638

46x + 12,740 - 28x = 15,638

(46x - 28x) +12,470 = 15,638

18x = 15,638-12,470= 3,168

divide both sides by 18 to isolate x we get,

x = 3,168/18 = 176 adult tickets

Substitute this value of x in equation1 or in equation2, whichever is simpler. In this case equation1 is much simpler.

So, x + y = 455 becomes

176 + y = 455

So, y = 455 -176 = 279 children's tickets