Question

At a hockey game, a vender sold a combined total of 168 sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

Answer 1

First we are going to set up two equations:

1) $x+y=168$

2) $y=3x$

where x is the number of hotdogs sold, and y is the number of sodas sold. Let's subtract x from the second equation and set equal to 0:

1) $x+y=168$

2) $3x-y=0$

Then let's add the two equations together to cancel out the y variable:

$x+y=168$

+ $3x-y=0$

---------------------------------

$4x=168$

Then solve for x:

$x=42$

So then return to equation 1 and plug in x to solve for y:

$x+y=168$

$42+y=168$

$y=126$

So then we know that x = 42 and y = 126; therefore, there were 42 hotdogs sold, and there were 126 sodas sold.