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Question

Adult tickets for a play cost $6 and child tickets cost $5. If there were 26 people at a performance and the theater collected $141 from ticket sales, how many children attended the play? Solve the system of equations using addition.

Answer 1

Let A be the number of adults attending the play
Let C be the number of children attending the play

A + C = 26
6A + 5C = 141

You need to make one of the terms the opposite, so multiply the top equation by -6. (You could also choose -5, but -6 will make the A terms cancel out. This saves you a step later on).

-6A + -6C = -156
6A + 5C = 141

Now add them together:
-C = -15

Multiply by -1 to reverse the signs:
C = 15

So you have 15 children.

(If you need to know the number of adults, just plug it back into the A + C = 26 equation, to figure you have 11 adults. A double-check shows that the cost of the tickets would be $6 x 11 + $5 x 15 = $141)

So the answer is 15 children (and 11 adults) attended the play.

Answer 2

have A = the # of adult tickets and C = # child tickets

A + C = 26 ( # kids plus # adults = amount of people total)
6A + 5C = 141

Take the first equation and solve for C:
A + C = 26
C = 26 - A

Now take this value of C and plug it into the second equation:
6A + 5C = 141
6A + 5(26 - A) = 141

now solve for A:
6A + 5(26 - A) = 141
6A + 130 - 5A = 141

combine like terms:
A + 130 = 141

subtract 130 from both sides
A = 11

There were 11 adults. Now plug this into the first equation to find how many children were there:
C + A = 26
C + 11 = 26

subtract 11 from both sides:
C = 15

there were 11 adults and 15 children

Answer 3

Make "a" the number of adults attending and "c" the number of children.

a + c = 26
6*a + 5*c = 141

Multiply the top row by -5

-5*a + -5*c = -130
6*a + 5*c = 141

Now add the rows

a + 0 = 11

a=11

Now go back to your first equation, a+c=26, and a=11, so c=15.

Answer 4

let x= # of adults & y= # of children

x=y=26 or x=26-y

6x+5y=141
6(26-y)+5y=141
-6y+5y+156=141
-y=-15
y=15
x=26-15=11

11 adults & 15 children

check

6*11+5*15=141
66+75=141
141=141

Answer 5

15 children

Answer 6

There were nine adults and seventeen children.