At a hockey game, a vender sold a combined total of 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.
got to know the total number sold. All you've said is that
s = 3h
you still need
s+h = ?
Fill in that value and then solve the two equations.
To find the number of sodas and hot dogs sold, let's use a system of equations.
Let's represent the number of sodas as 's' and the number of hot dogs as 'h'.
We are given that the number of sodas sold was three times the number of hot dogs sold, so we can write the equation:
s = 3h
We are also given that the combined total of sodas and hot dogs sold is a certain amount, but we don't know the exact value. Let's represent this total as 'x'.
We can write another equation for the combined total:
s + h = x
Now we have a system of two equations:
s = 3h (Equation 1)
s + h = x (Equation 2)
To solve this system, we can use the substitution method by substituting Equation 1 into Equation 2.
Substituting s = 3h into Equation 2, we get:
3h + h = x
4h = x (Equation 3)
We now have a new equation, Equation 3, which relates the number of hot dogs (h) to the combined total (x).
To find the number of sodas (s), we substitute the value of h in Equation 3 into Equation 1:
s = 3(4h)
s = 12h
Now we have two expressions for s: s = 12h from Equation 1, and s = 3h from Equation 3.
Since both expressions are equal to s, we can set them equal to each other:
12h = 3h
By dividing both sides of the equation by 3:
12h/3 = 3h/3
4h = h
We find that h = 0.
To find s, we substitute the value of h = 0 into any of the equations:
s = 3h
s = 3(0)
s = 0
So, the number of sodas sold (s) is 0, and the number of hot dogs sold (h) is also 0.
Therefore, according to the given information, no sodas or hot dogs were sold at the hockey game.