SOLUTION: five hot dogs and four burgers cost 14.75$. four hot dogs and 5 burgers cost 14.50$. Find the cost of one hot dog and the cost of one burger 5h+4b=14.75 4h+5b=14.50 First impres

Question 294640: five hot dogs and four burgers cost 14.75$. four hot dogs and 5 burgers cost 14.50$. Find the cost of one hot dog and the cost of one burger
5h+4b=14.75
4h+5b=14.50
First impression is to add them
9h+9b= 29.25
9(h+b)=29.25
h+b=29.25/9
but this makes no sense
Any help is greatly appreciated
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
five hot dogs and four burgers cost 14.75$. four hot dogs and 5 burgers cost 14.50$. Find the cost of one hot dog and the cost of one burger
5h+4b=14.75
4h+5b=14.50
First impression is to add them
----------------------------------------
The objective is to eliminate one of the variables.
----
To get rid of the "h" terms, multiply 1st equation by 4
and 2nd equation by 5 to get:
----
20h + 16b = 4*15.75
20h + 25b = 5*14.50
--------------------------
Now, SUBTRACT the 1st Eq. from the 2nd and solve for "b":
9b = 5*14.5 - 4*15.75
9b = 9.5
b = $1.06
----------------
To solve for "h", substitute b=1.06 into either of the original equations.
5h+4b=14.75
5h + 4(1.06) = 14.75
5h = 14.75-4.24
5h = 12.51
h = $2.50
===============
Cheers,
Stan H.
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