2/7 of the eggs at a store were quail eggs. 2/3 of the remaining eggs
were chicken eggs and the rest were duck eggs. The shopkeeper sold 3/5
of the chicken eggs, 1/2 of the quail eggs and 1/2 of the duck eggs. He
then had 104 chicken eggs left. How many eggs did he have left?
quail: 2/7 x
chicken: 2/3 * 5/7 = 10/21 x
duck: 5/21 x
2/5 * 2/7 x = 104
x = 910 at the start
Now you can finish it off
Let the total No. of eggs = x
∴ A/q
No. of quail eggs = 2x/7
Remaining eggs = x - 2x/7
∴ No. of chicken eggs = 2/3 (x - 2x/7)
And No. of duck eggs = (x - 2x/7) - 2/3 (x - 2x/7)
= 1/3 (x - 2x/7)
shopkeeper sold 3/5 of the chicken eggs.
∴ remaining chicken eggs = 2/3 (x - 2x/7)
- 2/3 * 3/5 (x - 2x/7)
=> 2x/3 - 4x/21 - 2x/5 + 4x/35 = 104 (A/q)
=> 70x - 20x - 42x + 12x/105 = 104
=> 20x = 10,920
=> x = 546 eggs. (Total eggs)
No. of quail egg = 2 * 546/7 = 156 egg
No. of duck egg = 1/3 (546 - 2 * 546/7)
= 130
shopkeeper sold 1/2 of the quail and 1/2
of the duck.
∴ Remaining eggs = 104 + 78 + 65
= 247 eggs.
He have left 247 eggs.
To solve this problem, we'll need to break it down step by step and keep track of the number of eggs at each stage.
Let's start with the total number of eggs at the store. We'll call this number "x."
According to the problem, 2/7 of these eggs were quail eggs. So, the number of quail eggs can be calculated by (2/7) * x.
The remaining eggs after the quail eggs were taken are (1 - 2/7) * x, which simplifies to (5/7) * x.
Then, 2/3 of these remaining eggs were chicken eggs, so the number of chicken eggs can be calculated by (2/3) * (5/7) * x.
The rest of the eggs were duck eggs, which can be calculated by subtracting the number of quail eggs and the number of chicken eggs from the total number of eggs. So, the number of duck eggs is x - [(2/7) * x + (2/3) * (5/7) * x].
Now, let's move on to the eggs that were sold.
The shopkeeper sold 3/5 of the chicken eggs, so the number of chicken eggs left after the sale is (1 - 3/5) * [(2/3) * (5/7) * x].
The shopkeeper sold 1/2 of the quail eggs, so the number of quail eggs left after the sale is (1 - 1/2) * [(2/7) * x].
The shopkeeper also sold 1/2 of the duck eggs, so the number of duck eggs left after the sale is (1 - 1/2) * [x - [(2/7) * x + (2/3) * (5/7) * x]].
According to the problem, the shopkeeper had 104 chicken eggs left. So,
(1 - 3/5) * [(2/3) * (5/7) * x] = 104
Now, we can solve for x and find the total number of eggs.