Algebra Word Problem

Question

A house cat weighs two more pounds than one fiftieth as much as a tiger.  What are the weights of the two creatures if the difference between their weights is 488 pounds.  

Answer 1

"cat weighs two more pounds than one fiftieth as much as a tiger" 

   means    c = (1/50)t + 2      [eq1]
"difference between their weights is 488 pounds"      means      t - c = 488             [eq2]

 

     -t  + 50c  =  100             [-50*eq1]

      t  -    c   =   488             [eq2]

 --------------------------        [elimination; add equations]

           49c   = 588

              c   =    12

       t   - c    =  488            [eq2 again]

 ------------------------         [elimination; add two equations]

      t            =   500

Answer 2

c = (1/50)t + 2

t - c = 488

 

The method that jumps out at me is substitution. Since c = t/50 - 2, we can plug (1/50)t - 2 in for c in the 2nd equation.

 

t - (1/50)t - 2)) = 488

(49/50)t + 2 = 488

(49/50)t = 490

(50/49)(49/50)t = 490(50/49)

t = 500

 

c = 500 - 488 = 12

 

That's a big housecat!