SOLUTION: adult tickets cost 8$ and student tickets for the concert cost 4$ exactly 290 tickets were sold and there was 1,440 made total how many students and adults tickets were sold

Algebra.Com
Question 1154228: adult tickets cost 8$ and student tickets for the concert cost 4$ exactly 290 tickets were sold and there was 1,440 made total how many students and adults tickets were sold
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(53937)   (Show Source): You can put this solution on YOUR website!
.

From the condition, you have this system of 2 equations in 2 unknowns

    x +  y =  290       (1)   (total number of tickets)

   8x + 4y = 1440       (2)   (total money)

where x = # of adult tickets,  y = # of student tickets.


From equation (1), express y = 290-x  and substitute it into equation (2), replacing y.  You will get then

    8x + 4*(290-x) = 1440.


From the last equation

    x =  = 70.


ANSWER.  70 adult tickets and 290-70 = 220 student tickets.


CHECK.   8*70 + 4*220 = 1440 dollars.   ! Correct !

Solved.

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

It is a standard tickets problem.

There are different methods of solving such problems.
In this site, there are lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) 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.


Answer by greenestamps(13367)   (Show Source): You can put this solution on YOUR website!


Formally....

a = number of adult tickets
s = number of student tickets

a+s = 290 (the total number of tickets was 290)
8a+4s = 1440 (the total cost, at $8 per adult and $4 per student, was $1440)

Solve the pair of equations by your favorite method....

When the equations are both in that form, elimination is easiest.

4a+4s = 1160
8a+4s = 1440

subtract one equation from the other to eliminate s

4a = 280
a = 70

There were 70 adult tickets.

So there were 290-70 = 220 student tickets.

ANSWER: 70 adult tickets, 220 student tickets.

CHECK: 70(8)+220(4) = 560+880 = 1440

Informally -- if an algebraic solution is not required....

(1) If all 290 tickets had been student tickets, the total cost would have been $290*4 = $1160; the actual total is $1440-$1160 = $280 more than that.
(2) The difference between the cost of an adult ticket and a student ticket is $4.
(3) The number of adult tickets needed to make up that extra $280 is 280/4 = 70.

ANSWER: 70 adult tickets and 220 student tickets

Note that the informal solution used exactly the same calculations as the formal method....
RELATED QUESTIONS

Adult tickets for a concert cost $8 each and student tickets cost $5 each. A total of 55... (answered by josgarithmetic)
There were 144 tickets sold for a movie. The ratio of the number of child tickets to the... (answered by josmiceli)
Solving systems of equations: The football team sold 60 tickets to their fundraiser... (answered by ikleyn)
at a school concert the total value of tickets sold was $994. Student tickets sold for $5 (answered by josgarithmetic)
For a school play, 340 tickets values at $810 were sold. Adult tickets cost $3 and... (answered by richwmiller)
Hello. School Plays: At a school play, 140 tickets were sold, with total receipts of... (answered by Zef)
After selling 550 adult and student tickets, the cashier at a theatre had receipts of... (answered by ewatrrr)
At the opening basketball game, 1000 tickets were sold. Adult tickets cost $3.00 and... (answered by josmiceli)
744 tickets were sold for a total of $4527, student tickets cost $5.5 and adult tickets... (answered by josmiceli)