A chef had some eggs. He used 1/7 of them on Monday and 1/11 of the rest on Tuesday. He bought another 153 eggs and then had as many eggs as he had at first. How many eggs did he have at first?
1/7 x + 1/11 * 6/7 x = 153
now just solve for x
𝑥 = 693
To find the number of eggs the chef had at first, we need to go step by step:
Let's assume the number of eggs the chef had at first is represented by "x".
On Monday, the chef used 1/7 of the eggs, which is (1/7) * x = x/7.
The eggs that remained after Monday are (1 - 1/7) of the original amount, which is 6/7 of x.
On Tuesday, the chef used 1/11 of the remaining eggs, which is (1/11) * (6/7) * x = 6x/77.
After Tuesday, the eggs that remained are (1 - 1/11) of the previous amount, which is 10/11 of 6x/77.
According to the problem, the chef then bought another 153 eggs, which results in 10/11 * 6x/77 + 153 = x.
Simplifying this equation will help us find the value of x.
Let's multiply both sides of the equation by 11 * 77 to eliminate the denominators:
10 * 6x + 153 * 11 * 77 = x * 11 * 77.
Simplifying further, we get:
60x + 153 * 847 = 77x.
Now, let's isolate x on one side of the equation:
60x - 77x = -153 * 847.
Simplifying again:
-17x = -153 * 847.
Dividing both sides by -17:
x = (-153 * 847) / -17.
Calculating this expression will give us the answer.