A vendor has some eggs.4 eggs were broken. Half the remaining were sold out. In that 30 eggs were remaining at the end of the day. How many eggs he start with
If he started with x, then
(x-4)/2 = 30
Thank you Steve , Accurate equation.
The answer is 64.
Let's break down the problem step by step:
1. Start with the total number of eggs the vendor had initially.
2. Subtract the number of eggs that were broken - 4 eggs.
3. Calculate half of the remaining eggs.
4. Subtract the number of eggs sold - which is half of the remaining eggs.
5. Verify if the result is 30 eggs left at the end of the day.
Let's write down each step in the calculation:
Let "x" be the total number of eggs the vendor started with.
1. Total number of eggs: x
2. Eggs after subtracting broken eggs: x - 4
3. Half of the remaining eggs: (x - 4) / 2
4. Eggs after subtracting the sold eggs: (x - 4) / 2 - sold eggs
5. Verify if the remaining eggs equal 30: (x - 4) / 2 - sold eggs = 30
We need additional information about how many eggs were sold in order to solve the equation.
To find out how many eggs the vendor started with, let's work through the information provided step by step.
1. We know that 4 eggs were broken. So, let's subtract these broken eggs from the total count.
Eggs remaining after breakage = Total eggs - Broken eggs
= Total eggs - 4
2. It is mentioned that half of the remaining eggs were sold out. This means that the number of eggs sold is equal to half of the remaining eggs.
Eggs sold = (Remaining eggs) / 2
3. It is stated that there were 30 eggs remaining at the end of the day. So, we can equate this to the number of eggs remaining after breakage minus the number of eggs sold.
30 = (Remaining eggs after breakage) - (Eggs sold)
Now, we have two equations, one from step 1 and another from step 3. We can combine them to find the total number of eggs the vendor started with.
Total eggs - 4 = 30 + Eggs sold
Since Eggs sold = (Remaining eggs after breakage) / 2, we can substitute this value in the equation.
Total eggs - 4 = 30 + (Remaining eggs after breakage) / 2
Simplifying the equation:
Total eggs - 4 = 30 + (Total eggs - 4) / 2
Multiply both sides by 2 to eliminate the fraction:
2 * (Total eggs - 4) = 60 + Total eggs - 4
2 * Total eggs - 8 = 60 + Total eggs - 4
Rearranging the equation:
Total eggs - Total eggs/2 = 64
Simplifying further:
Total eggs/2 = 64
Multiply both sides by 2:
Total eggs = 2 * 64
Total eggs = 128
Therefore, the vendor started with 128 eggs.