A vendor sold 2/3 of his hot dogs in the morning and 1/6 in the afternoon. He sold 200 hot dogs altogether. How many hot dogs does he have left?
2/3 + 1/6 = 4/6 + 1/6 = 5/6
(5/6) * x = 200
x = 200 / (5/6) = 200 * (6/5) = 1200/5 = 240
40 hot dogs are left.
To find out how many hot dogs the vendor has left, we need to determine how many he sold in total and subtract that number from his original stock.
Let's calculate how many hot dogs the vendor sold in the morning:
2/3 of the hot dogs were sold in the morning. If we let x represent the total number of hot dogs, then the equation for the hot dogs sold in the morning is (2/3)x.
Next, let's determine how many hot dogs the vendor sold in the afternoon:
1/6 of the hot dogs were sold in the afternoon. Since we already know that 200 hot dogs were sold altogether, the equation for the hot dogs sold in the afternoon is (1/6)x.
To find the value of x, we can set up an equation: (2/3)x + (1/6)x = 200.
To solve this equation, we can find a common denominator for the fractions, which is 6:
(4/6)x + (1/6)x = 200.
Adding the fractions, we get: (5/6)x = 200.
To isolate x, we multiply both sides of the equation by (6/5):
x = 200 * (6/5).
Simplifying the expression, we find: x = 240.
So the vendor originally had 240 hot dogs.
Now, to determine how many hot dogs he has left, we subtract the number of hot dogs sold from the original stock:
240 - 200 = 40.
Therefore, the vendor has 40 hot dogs left.
To find the number of hot dogs the vendor has left, we need to subtract the number of hot dogs he sold from the total number of hot dogs he had initially.
First, let's calculate the number of hot dogs he sold in the morning. The vendor sold 2/3 of his hot dogs, which can be represented as (2/3) * Total_hot_dogs = Hot_dogs_sold_in_morning.
Similarly, the number of hot dogs sold in the afternoon can be represented as (1/6) * Total_hot_dogs = Hot_dogs_sold_in_afternoon.
According to the problem, the total number of hot dogs sold is 200. Therefore, we can set up an equation:
Hot_dogs_sold_in_morning + Hot_dogs_sold_in_afternoon = 200.
Substituting the respective equations, we get:
(2/3) * Total_hot_dogs + (1/6) * Total_hot_dogs = 200.
To solve this equation, we can first find a common denominator for (2/3) and (1/6), which is 6. Rewriting the equation:
(4/6) * Total_hot_dogs + (1/6) * Total_hot_dogs = 200.
Combining like terms:
(5/6) * Total_hot_dogs = 200.
To isolate Total_hot_dogs, we can multiply both sides of the equation by (6/5):
Total_hot_dogs = (200 * 6) / 5 = 240.
So, the vendor initially had 240 hot dogs.
To find the number of hot dogs he has left, we subtract the total number of hot dogs sold from the initial number of hot dogs:
Hot_dogs_left = Total_hot_dogs - Hot_dogs_sold_in_morning - Hot_dogs_sold_in_afternoon.
Hot_dogs_left = 240 - ((2/3) * 240) - ((1/6) * 240).
Hot_dogs_left = 240 - 160 - 40.
Hot_dogs_left = 40.
Therefore, the vendor has 40 hot dogs left.