Substitution Math

Question

Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 20 more adult tickets than student tickets to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold? Thanks!

Answer 1

Substitution.

Adult tickets = A (cost $8)

student tickets = S (cost $4)

 

The drama class sold 20 more adult tickets than student tickets:

A = S + 20 (equation 1)

 

The class collected $880 from tickets:

8A + 4S = 880 (equation 2)

 

How many adult tickets were sold?

A = S + 20

8A + 4S = 880

 

we substitute the first equation into the second:

8(S+20) + 4S = 880 

8S + 160 + 4S = 880

12S = 720

S = 60

 

Next we find the adult tickets by substituting back:

 A = S + 20

 A = 60 + 20

 A = 80

 

Check our answer by substituting our answers in equation 2:

8A + 4S = 880 (equation 2)

8(80) + 4(60) = 880

640 + 240 = 880

880 = 880

Answer 2

The two equations are 8x+4y=880 (the value of the tickets) and y-20=x (the total number of adult tickets minus 20 equals the number of student tickets). Sub in y-20 for the x in the first equation and solve.

Answer 3

My advice that I have been teaching and stressing for solving ANY word problem:

 

#1.   Draw a diagram or some type of picture of the situation!  This is probably the most important, but also the easiest! 

 

#2.   Use a variable (such as x or y, but it could be any letter you choose) for something that is unknown or being asked for.

 

#3.   Write down an equation, in WORDS, that you can come up with.  And that can be anything--usually it's very obvious.    Remember, all you need to write an equation in  words is to use the word "IS"/

 

#4.   Translate those words into an algebraic equation,  remembering that "is" means equals or = and the word "of means "times" or multiply.    If you have percents, those mean "hundreths". 

 

#5.    Solve that equation for your variable.

 

And if you introduce two variables (which is OK), you will need two equations.   Three variables requires three different equations.  Four variables need four equations, and so on.