Algebra Problem Solver

Question

Chris and Dominic went to a Justin Bieber concert. Chris purchased 2 t shirts and a bobble head and it cost $101.25. Dominic purchased 3 t shirts and 2 bobble heads for $138.75. If Nicole wants to purchase 1 shirt and1 bobble head, how much will she spend?

Answer 1

Let t=price of a t-shirt
     b=price of a bobble head
 
     Chris:     2t + 1b  = $101.25
 
                   4t + 2b = $202.50      (multiply Chris' equation by 2)
Dominic:      3t + 2b  =  138.75
                   ----------------------
                    t          =  $63.75      (subtract the equations; call this eq. E)
 
                   2t  + 1b = $101.25
                   2t          = $127.50      (multiply eq. E by 2)
                   ----------------------
                             b = -$26.25    (subtract the equations; then think!!)
 
What?  The're paying them to buy bobble heads?  There must be a BIG discount here somewhere -- Nicole might want to change her order!  (For those who need a math explanation, this means that the cost of t-shirts and the cost of bobble heads cannot be positive constants.)
  
Just thinking:  1.5 times Chris's purchase would be 3 t-shirts and 1.5 bobble heads for roughly $150, but Dominic got a better deal than that -- he got 2 bobble head -- and his total was only $138.75.
 
So, if you proceed blindly (or are asleep), you could believe that Nicole could buy 1 t-shirt ($63.75) and 1 bobble head (get 26.25 back) for a total of $37.50.  And, if she just wanted a t-shirt, it would be cheaper to buy both and throw the bobble head away (but PLZ don't re-sell it for -$26.25).

Answer 2

If t = price of t-shirt
and b = price of bobble head,

then
Chris --> 2t + b = 101.25
Dominic --> 3t + 2b = 138.75

Rearrange Chris' equation to solve for b, so:
b = 101.25 - 2t

Use substitution and plug b into Dominic's equation:
3t + 2(101.25 -2t) = 138.75
3t + 202.50 - 4t = 138.75
202.46 - t = 138.75
- 202.50     -202.50
-t = -63.75
t = 63.75

Plug in t and solve for b.

b = 101.25 - 2*63.75 = -26.25

Therefore Nicole --> t + b = 63.75 - 26.25 = 37.50