The concession stand sells hot dogs and drinks during their high school foot ball game. John bought 6 hot dogs and 4 drinks and paid $6.70. Jessica bought 4 hot dogs and 3 drinks and paid $4.65. What is the price of a hot dog?

Question

The concession stand sells hot dogs and drinks during their high school foot ball game. John bought 6 hot dogs and 4 drinks and paid $6.70. Jessica bought 4 hot dogs and 3 drinks and paid $4.65.  What is the price of a hot dog?

anonymous · Answer

Let the price of price of a hot dog and a drink be x and y dollars respectively
therefore, converting '6 hot dogs and 4 drinks and paid $6.70' into equation we find
6x+ 4y=6.70 -----(1
 similarly, converting ' 4 hot dogs and 3 drinks and paid $4.65' into equation we find
4x+ 3y=4.65 -----(2

Now in order to solve the simultaneous eq we need to eliminate at least on variable, so w multiply eq 1 by 2 and eq 2 by 3 and then subtracting  1 from 2 
 we have 
12x+ 8y=13.40 -----(1

12x+ 9y=13.95 -----(2
-    -        -
-----------------------
0-y=     -0.55
i.e. y= 0.55 
substituting y= 0.55 in eq 1 we find 
6x+ 4*0.55=6.70 -----(1
6x+ 2.2=6.70
6x= 6.70-2.2
6x= 4.5
x= 4.5/6
x=0.75
Thus, the price of a hot dog is $0.75