SOLUTION: A total of 290 people attended the highschool play. The admission prices were $11 for​ adults, $7 for high school​ students, and $2 for children not yet in high school.

Algebra.Com
Question 1119317: A total of 290 people attended the highschool play. The admission prices were $11 for​ adults, $7 for high school​ students, and $2 for children not yet in high school. The ticket sales totaled $1750. The principal suggested that next year they raise prices to $15 for​ adults, $8 for high school​ students, and $3 for children not yet in high school. He said that if exactly the same number of people attend next​ year, the ticket sales at the higher prices will total $2280. How many​ adults, high school​ students, and children not yet in high school attended this​ year?
Found 3 solutions by ikleyn, greenestamps, Shin123:
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.
The condition gives you this system of equations.


  x +  y +  z =  290    (1)   ( x = #adults, y = #high school students, z = #children)
11x + 7y + 2z = 1750    (2)
15x + 8y + 3z = 2280    (3)


To solve it, I used the online free of charge solver at this site

    https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver

    https://www.algebra.com/algebra/homework/Matrices-and-determiminant/cramers-rule-3x3.solver

which employed the Cramer's rule.


Answer.  x = 80,  y = 90,  z = 120.


Other method (Elimination) also works. You may try it.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


If you don't have access to a tool that solves systems of equations for you, you are stuck with having to do a pencil-and-paper solution.

For a general system of three linear equations, this can be very tedious.

However, in a timed competitive exam (for example), there will usually be a way of combining the given equations to make the solution relatively easy. So look at the coefficients in the given equations and see if you can see a way to combine them to perhaps eliminate one of the variables.

The system of equations for this problem is





In this system, I immediately see the "z", "2z" and "3z" in the three equations; if I add the first two equations and compare the resulting equation to the third, variable z will be eliminated.






I got a bonus this time -- I eliminated TWO variables at once, allowing me to immediately find the value of the third.

Plugging the value of x into the first two of the original equations, we get




Double the first equation and compare to the second to eliminate z:







Answer: x = 80 (adults); y = 90 (high school students); z = 120 (younger students)
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
RELATED QUESTIONS

A total of four hundred people attended the local symphony's holiday concert at the civic (answered by josgarithmetic)
There were 610 people at a play. The admission price was $3.00 for adults and $1.00 for... (answered by nerdybill)
there were 620 people at a play. The admission was $2 for adults and $1 for children. The (answered by josgarithmetic)
A total of 434 people attended a community theatre performance. The admission prices... (answered by Edwin McCravy,ankor@dixie-net.com)
There were 411 people at a play. Admission was $1.00 for adults and $.75 for children.... (answered by checkley77)
the drama club sold 1500 tickets for the end of the year performance. admission prices... (answered by Fombitz)
The drama club sold 1,500 tickets for the end-of-year-performance. Admission prices were... (answered by jim_thompson5910)
There were 590 people at play. the admission price was $3.00 for adults and $1.00 for... (answered by Jstrasner)
There were 360 people at a play. The admission price was $2 for adults and $1 for... (answered by ewatrrr)