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 ->
Customizable Word Problem Solvers
-> Misc
-> 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.
Log On
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(52781) (Show Source):
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.
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)
