SOLUTION: Word problems are my weakness, please help Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $30. F

Question 1171608: Word problems are my weakness, please help
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $30. For one performance, there were 40 tickets sold in all, and the total amount paid for them was $1325. How many tickets of each type were sold?
Found 3 solutions by Boreal, math_tutor2020, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
number equation Advance=A;Same day=S
we know A+S=40
so S=40-A (can also say A=40-S, but use only one form)
money equation is 35A+30S=1325
substitute 40-A for S
so 35A+30(40-A)=1325
35+1200-30A=1325
5A=125
A=25 tickets or $875 total
S=15 tickets or $450 total
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = number of advance tickets sold
y = number of same-day tickets sold
x and y are placeholders for nonnegative whole numbers

The first equation is x+y = 40 because the instructions state "there were 40 tickets sold in all".

Let's solve for y to get y = 40-x. I subtracted x from both sides.

----------------------------------

1 advance ticket costs $35
x advance tickets cost 35x dollars
eg: if you sold x = 10 advance tickets then 35*x = 35*10 = 350 dollars is earned from these tickets alone

1 same-day ticket costs $30
y of these tickets costs 30y dollars
eg: if you sold y = 20 same-day tickets then 30*y = 30*20 = 600 dollars is earned from these tickets alone

In total we have 35x+30y dollars earned from both types of tickets combined.

We're told that "The total amount paid for them was $1325" so 35x+30y = 1325 is the second equation.

----------------------------------

The system of equations we have is
y = 40-x
35x+30y = 1325

We can use substitution to solve
35x+30y = 1325

35x+30( y ) = 1325

35x+30( 40-x ) = 1325 .... y replaced with 40-x

35x+30( 40 ) + 30( -x ) = 1325

35x+1200-30x = 1325

5x+1200 = 1325

5x+1200-1200 = 1325-1200 .... subtract 1200 from both sides

5x = 125

5x/5 = 125/5 .... dividing both sides by 5

x = 25

There were 25 advance tickets sold.

Use this to find y
y = 40-x

y = 40-25

y = 15

There were 15 same-day tickets sold.

As a check,
x+y = 25+15 = 40
helps show that 40 tickets were sold
This confirms the first equation.

And also,
35x = 35*25 = 875 dollars earned from advance tickets only
30y = 30*15 = 450 dollars earned from same-day tickets only
35x+30y = 875+450 = 1375 dollars earned in total
This confirms the second equation.

Since both equations have been satisfied, this confirms our answers.

----------------------------------

Answers:
25 advance tickets sold
15 same-day tickets sold

Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
.

Let x be the number of advance tickets. Then the number of same-day tickets is (40-x), OBVIOUSLY. Next, you write the total money equation 35x + 30*(40-x) = 1325 (total money). It is your basic equation for this problem. As soon as you understand on how to get it and how to write it, the setup is complete and you are a winner. The rest is just a technique. To solve the equation, simplify it 35x + 1200 - 30x = 1325 35x - 30x = 1325 - 1200 5x = 125 x = 125/5 = 25. ANSWER. 25 advanced tickets and (40-25) = 15 same-day tickets. CHECK. 25*35 + 15*30 = 1325, total money. ! Precisely correct !

The problem is just solved.

Please let me know if everything is clear to you in my solution.

Do not hesitate to ask questions, if you have some.

---------------

It is a standard and typical tickets problem.

There are different methods of solving such problems.
In this site, there is a lesson
    - Using systems of equations to solve problems on tickets
explaining and showing all basic methods of solving such problems.

From these lessons, learn on how to solve such problems once and for all.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

/\/\/\/\/\/\/\/

In studying word problems, the major thing is to learn it from a good source.

Please do not forget to post your "THANKS" to me for my teaching.

RELATED QUESTIONS
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by josgarithmetic)
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by josgarithmetic)
Problem Page Suppose that there are two types of tickets to a show: advance and same-day. (answered by ikleyn)
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by josgarithmetic)
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by josgarithmetic)
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by josgarithmetic)
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by josgarithmetic,greenestamps)
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by ikleyn)
Suppose that there are two types of tickets to a show: advance and same-day. The combined (answered by Theo,ikleyn)