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 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?
5 answers
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.
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.
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.
2 answers