How many kid's tickets did the group purchase?

Question

Tickets to the movies cost $9.50 for adults and $6.50 for kids. A large group brought 12 tickets and spent a total of $87. How many kid's tickets did the group purchase?

Answer 1

So let X = the number of adult tickets and Y = the number of kids' tickets

The total number of tickets is 12

Thus X + Y = 12 .......................Equation 1

The total cost for adult tickets is $9.5 times X or 9.5X dollars

The total cost for kids' tickets is $6.5 times Y or 6.5Y dollars

Since $87 was the total cost then

9.5X + 6.5Y = 87 .........................Equation 2

So now we have two equations in two unknowns (X and Y). We can solve for the X and Y in different ways. We will use the method of substitution in this case.

Since the question asks for the number of kids' tickets we will solve for Y. From Equation 1, let's find X

X + Y = 12

Subtract Y from both sides to get X + Y - Y = 12 - Y

Thus X = 12 - Y .............Equation 3

Substituting Equation 3 in Equation 2 we get

9.5(12-Y) + 6.5Y = 87

9.5*12 - 9.5*Y + 6.5Y = 87 (We are using the * symbol to denote multiplication)

114 - 3Y = 87

subtract 114 from both sides to get

114-3Y - 114 = 87 - 114

-3Y = -27 and dividing both sides by -3 we get

-3Y/-3 = = -27/-3

Y = 9 or the total number kids' tickets is 9 is your answer.

You can quickly check your answer to see. Total tickets were 12 so the adults tickets were then 3 from

(12 -9)

And for the cost you have 9.5*3 + 6.5*9 = 28.5 + 58.5 = $87

Answer 2

a represents the number of adult tickets

12 - a represents the number of kid tickets

9.5a + 6.5(12 - a) = 87

Can you solve for a and answer?