At a hockey game, a vender sold a combined total of
248
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.
hot dogs ---- x
sodas ----- 3x
x + 3x = 248 , solve for x and evaluate 3x
Let's solve this problem step by step.
Step 1: Assign variables
Let's assume the number of hot dogs sold as "x".
Since the number of sodas sold is three times the number of hot dogs sold, we can assign the number of sodas sold as "3x".
Step 2: Formulate the equation
We know that the combined total of sodas and hot dogs sold is 248.
So, we can write the equation as:
x + 3x = 248
Step 3: Simplify the equation
Combine like terms on the left side of the equation:
4x = 248
Step 4: Solve for x
Divide both sides of the equation by 4:
x = 248/4
x = 62
Step 5: Calculate the number of sodas sold
Since the number of sodas sold is three times the number of hot dogs sold, we can calculate it as:
3x = 3 * 62
3x = 186
Therefore, the number of sodas sold is 186.
Step 6: Calculate the number of hot dogs sold
Since we already found that "x" is 62, we can conclude that the number of hot dogs sold is 62.
To summarize, the number of sodas sold is 186 and the number of hot dogs sold is 62.
To solve this problem, we can set up a system of equations based on the information given. Let's use variables to represent the number of sodas and hot dogs sold.
Let's say the number of hot dogs sold is "x". Since the number of sodas sold is three times the number of hot dogs sold, we can say the number of sodas sold is 3x.
Now, we can set up an equation to represent the combined total of sodas and hot dogs. We know that the combined total is 248, so we can write the equation as:
x + 3x = 248
Combining like terms, we get:
4x = 248
To find the value of x, we can divide both sides of the equation by 4:
x = 248/4
x = 62
Therefore, the number of hot dogs sold is 62.
To find the number of sodas sold, we can substitute the value of x back into the equation:
Number of sodas sold = 3x = 3 * 62 = 186
So, the number of sodas sold is 186.
In summary, the number of sodas sold is 186 and the number of hot dogs sold is 62.