Dan helps his father selling fish balls in the market. He sold 90 of them in the morning and 1/3 of the remainder in the afternoon. If he still had 1/2 of the stock left at the end of the day, how many fish balls were there in the stall at first?
Dan sold a total of 90 + 1/3(90) = <<90+1/3*90=120>>120 fish balls in the morning and afternoon.
His stock by the end of the day was 1/2(120) = <<120*1/2=60>>60 fish balls.
Therefore, there were 60 x 2 = <<60*2=120>>120 fish balls in the stall at first. Answer: \boxed{120}.
Dan sold 90 fish balls in the morning, so that leaves (360 - 90) = 270 fish balls left.
In the afternoon, he sold 1/3 of the remaining fish balls, so that's (270/3) = 90 fish balls.
That leaves (270 - 90) = 180 fish balls left at the end of the day.
Since Dan had 1/2 of the stock left at the end of the day, that means he originally had (180 * 2) = 360 fish balls in the stall.
Sorry, but I made an error in my previous response. You are correct in your calculations. Dan originally had 360 fish balls in the stall.
To find the initial number of fish balls in the stall, we can work backwards from the information given. Let's break down the problem step by step.
First, Dan sold 90 fish balls in the morning. This means that the remainder of fish balls in the stall after the morning sales is the initial stock minus 90.
Next, Dan sold 1/3 of the remainder in the afternoon. Since 1/3 of the remainder was sold, this means that 2/3 of the remainder is left at the end of the afternoon. Therefore, we can set up an equation:
2/3 * (initial stock - 90) = 1/2 * initial stock
To solve this equation, we can multiply both sides by 6 to get rid of the fractions:
4 * (initial stock - 90) = 3 * initial stock
Expanding both sides:
4 * initial stock - 360 = 3 * initial stock
Subtracting 3 * initial stock from both sides:
initial stock - 360 = 0
Adding 360 to both sides:
initial stock = 360
Therefore, there were initially 360 fish balls in the stall.
Apologies for the incorrect calculation in my previous response. You are correct, there were initially 360 fish balls in the stall.
Let's work step by step to solve this problem.
Step 1: Calculate the total number of fish balls sold in the morning.
Dan sold 90 fish balls in the morning.
Step 2: Calculate the remaining fish balls after the morning sales.
Let's assume the total number of fish balls at the beginning of the day was 'x'.
The remaining fish balls after the morning sales would be: x - 90.
Step 3: Calculate the number of fish balls sold in the afternoon.
Dan sold 1/3 of the remaining fish balls in the afternoon.
So, the number of fish balls sold in the afternoon is: (1/3) * (x - 90).
Step 4: Calculate the remaining fish balls at the end of the day.
The remaining fish balls at the end of the day is 1/2 of the initial stock.
So, (1/2) * x.
According to the given information, the remaining fish balls at the end of the day is equal to (1/2) * x.
So, (1/2) * x = (x - 90) - (1/3) * (x - 90).
Step 5: Solve the equation to find the value of 'x'.
(1/2) * x = (3/3) * (x - 90) - (1/3) * (x - 90).
(1/2) * x = (3x - 270) / 3 - (x - 90) / 3.
(1/2) * x = (3x - 270 - x + 90) / 3.
(1/2) * x = (2x - 180) / 3.
Multiplying both sides of the equation by 2:
x = (4x - 360) / 3.
Multiplying both sides of the equation by 3 to eliminate the denominator:
3x = 4x - 360.
Subtracting 4x from both sides of the equation:
- x = - 360.
Multiplying both sides of the equation by -1 to solve for x:
x = 360.
Therefore, there were a total of 360 fish balls in the stall at first.
To find out how many fish balls were there in the stall at first, we can follow these steps:
1. Start by finding the total number of fish balls sold in the morning. According to the given information, Dan sold 90 fish balls in the morning.
2. Next, calculate the remaining fish balls that Dan had after the morning sales. Since he had 1/2 of the stock left at the end of the day, we know that 1/2 of the fish balls were remaining. So, the remainder after the morning sales is 1/2 times the total number of fish balls.
3. Now, let's calculate the number of fish balls sold in the afternoon. It is mentioned that Dan sold 1/3 of the remainder in the afternoon. So, we can calculate 1/3 times the remainder calculated in the previous step.
4. To find the initial number of fish balls, we need to add the morning sales, afternoon sales, and the remaining fish balls. This will give us the total number of fish balls at the start of the day.
Let's do the calculations:
1. Fish balls sold in the morning: 90
2. Remaining fish balls: 1/2 * total number of fish balls
3. Fish balls sold in the afternoon: 1/3 * remaining fish balls
4. Total number of fish balls = Morning sales + Afternoon sales + Remaining fish balls
Calculating the total number of fish balls:
Total number of fish balls = 90 + (1/3 * (1/2 * total number of fish balls)) + (1/2 * total number of fish balls)
Now we can solve this equation to find the total number of fish balls. Let's simplify and solve it:
Total number of fish balls = 90 + (1/6 * total number of fish balls) + (1/2 * total number of fish balls)
Combining the like terms:
Total number of fish balls = 90 + (8/6 * total number of fish balls)
To eliminate the fractions, we multiply the entire equation by 6:
6 * Total number of fish balls = (540 + 8 * total number of fish balls)
Distribute 8 to the terms in the parentheses:
6 * Total number of fish balls = 540 + 8 * total number of fish balls
Multiply 8 by the total number of fish balls:
6 * Total number of fish balls = 540 + 8 * total number of fish balls
Rearrange the equation to isolate the total number of fish balls:
6 * Total number of fish balls - 8 * Total number of fish balls = 540
Combine the like terms:
-2 * Total number of fish balls = 540
Divide both sides by -2:
Total number of fish balls = -540 / -2
Total number of fish balls = 270
Therefore, there were 270 fish balls in the stall at first.