At a hockey game, a vender sold a combined total of 213 sodas and hot dogs. The number of hot dogs sold was 37 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Let's assume the number of sodas sold as 'x'.
According to the given information, the number of hot dogs sold is 37 less than the number of sodas sold. So, the number of hot dogs sold can be represented as 'x - 37'.
The total number of sodas and hot dogs sold is 213. So, we can form the equation:
x + (x - 37) = 213
Simplifying the equation, we get:
2x - 37 = 213
Adding 37 to both sides of the equation:
2x = 213 + 37
2x = 250
Dividing both sides of the equation by 2:
x = 250/2
x = 125
Therefore, the number of sodas sold is 125.
The number of hot dogs sold can be calculated as:
x - 37 = 125 - 37 = 88
So, the number of hot dogs sold is 88.
To find the number of sodas sold and the number of hot dogs sold, we can set up a system of equations based on the given information. Let's call the number of sodas "s" and the number of hot dogs "h".
From the problem, we know that the total number of sodas and hot dogs sold is 213. Therefore, our first equation is:
s + h = 213
We are also told that the number of hot dogs sold is 37 less than the number of sodas sold. This can be represented as:
h = s - 37
Now we have two equations:
s + h = 213
h = s - 37
To solve this system of equations, we can use substitution or elimination. Let's use substitution here:
Substitute the expression of h from the second equation into the first equation:
s + (s - 37) = 213
Combine like terms:
2s - 37 = 213
Add 37 to both sides of the equation:
2s = 213 + 37
2s = 250
Divide both sides of the equation by 2:
s = 250 / 2
s = 125
Now that we know the number of sodas sold, we can substitute this value back into one of the original equations to find the value of h:
h = s - 37
h = 125 - 37
h = 88
So, the number of sodas sold is 125, and the number of hot dogs sold is 88.
if there were s sodas sold, then
s + s-37 = 213
solve for s, then h=s-37