At a hockey game, a vender sold a combined total of 117 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
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To find the number of sodas and hot dogs sold, let's set up a system of equations.
Let's call the number of sodas 'S' and the number of hot dogs 'H'.
We know that the combined total of sodas and hot dogs sold is 117:
S + H = 117 -- Equation 1
We're also given that the number of sodas sold was two times the number of hot dogs sold:
S = 2H -- Equation 2
To solve this system of equations, we can use the substitution method.
Substitute Equation 2 into Equation 1:
2H + H = 117
Combine like terms:
3H = 117
Divide both sides by 3 to solve for H:
H = 117 / 3
H = 39
Now, substitute the value of H back into Equation 2 to find S:
S = 2(39)
S = 78
Therefore, the number of sodas sold is 78, and the number of hot dogs sold is 39.
Let's assume the number of hot dogs sold as 'x'.
According to the problem statement, the number of sodas sold is twice the number of hot dogs sold, so the number of sodas sold can be represented as 2x.
The total number of sodas and hot dogs sold is given as 117, so we can form an equation:
x + 2x = 117
Combining like terms:
3x = 117
To solve for x, we divide both sides of the equation by 3:
x = 117/3
x = 39
So, the number of hot dogs sold is 39.
Now, to find the number of sodas sold, we substitute the value of x back into the equation:
2x = 2 * 39
2x = 78
Therefore, the number of sodas sold is 78.
In conclusion, the number of sodas sold is 78 and the number of hot dogs sold is 39.