SOLUTION: at a baseball game, a vendor sold a combined total of 175 sodas and hot dogs. the number of sodas sold was 51 more than the number of hot dogs sold. find the number of sodas and th

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: at a baseball game, a vendor sold a combined total of 175 sodas and hot dogs. the number of sodas sold was 51 more than the number of hot dogs sold. find the number of sodas and th      Log On


   

Question 1114421: at a baseball game, a vendor sold a combined total of 175 sodas and hot dogs. the number of sodas sold was 51 more than the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
H%2BS=175
and
S=51%2BH
Substituting,
H%2B%2851%2BH%29=175
2H=124
Solve for H, then use either equation to solve for S.

Answer by ikleyn(52896) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.   Two equations setup and solution 


    S + D = 175      (1)
    S - D =  51      (2)
   ---------------------------  Add the equations to eliminate D:


   2S     = 175 + 51 = 226  ====>  S = 226%2F2 = 113  (the number of sodas)


   Then the number of dogs, from eq(1),  D = 175 - S = 175 - 113 = 62.


Answer.  113 sodas and 62 dogs.


2.   One equation setup and solution 

sodas + dogs   = 175


S     + (S-51) = 175


2S - 51 = 175  ====>  2S = 175 + 51 = 226  ====>  S = 226%2F2 = 113,


And you get the same answer.