Question

You and your friend are selling tickets to a charity event. You sell 9 adult tickets and 13 student tickets for 212$. Your friend sells 4 adult tickets and 15 student tickets for $168.What is the cost of student ticket?

Answer 1

$8

Explanation:

Let a and s represent the prices of adult and student tickets, respectively. The relations described by the problem statement can be written ...

9a +13s = 212

4a +15s = 168

Using Cramer's method, we can find the value of s to be ...

s = (212·4 -168·9)/(13·4 -15·9) = -664/-83 = 8

The price of a student ticket is $8.

_____

Comment on Cramer's method

For the equations ...

• ax +by = c
• dx +ey = f

the solutions can be written as ...

• ∆ = bd-ea
• x = (bf-ec)/∆
• y = (cd-fa)/∆

This method is useful when the equation's coefficients don't lend themselves to "nice" arithmetic or when the value of only one variable is needed (as here).

__

If you look up "Cramer's Method" in Wikipedia or other sources, you will likely find that the signs of the differences are reversed. That is, ...

x = (ce-bf)/(ae-bd)

This makes no difference to the result of the calculation. The variable ordering shown here can be remembered as a pattern of Xs when compared to the locations of the coefficients in the given equations. Often, this permits the problem to be completely solved mentally.