At a hot dog stand, there is a fixed price for hot dogs and a different price for sift drinks. 1 person bought 3 hot dogs and 2soft drinks for $9.25.Aperson ahead bought 2 hot dogs and 1 soft drink. How much does 1 hot dog cost?
I need help understanding why the right answer is $2.25

Question

At a hot dog stand, there is a fixed price for hot dogs and a different price for sift drinks. 1 person bought 3 hot dogs and 2soft drinks for $9.25.Aperson ahead bought 2 hot dogs and 1 soft drink. How much does 1 hot dog cost? 
I need help understanding why the right answer is $2.25

alexrobin13 · Answer

How much did the second purchase cost?

ellecullen · Answer

$5.75

alexrobin13 · Answer

Okay so let x be hot dogs and r be soft drinks. 
3x+2y=9.25    2x+1y=5.75

alexrobin13 · Answer

To find how much a hot dog costs, you need to isolate y in each equation.

alexrobin13 · Answer

So 
3x+2y=9.25
2y=9.25-3x
y=(9.25-3x)/2

alexrobin13 · Answer

And
2x+y=5.75
y=5.75-x

alexrobin13 · Answer

Since y=y, you can set the second half of both of these equations together

alexrobin13 · Answer

So
y=y
(9.25-3x)/2=5.75-2x
9.25-3x=11.50-4x
x=11.50-9.25
x=2.25
So there you go :)