There are ten children standing in the line, not all of whom have the same number of cakes with them. If the first child distributes his cakes to the remaining six children such that he doubles their respective number of cakes, then he will be left with four cakes. Instead, if the second child takes away two cakes from each of the remaining six children, then he will be left with three cakes less than the number of cakes that the first child initially had. What is the total number of cakes that are there with the third to the seventh child

Question

There are ten children standing in the line, not all of whom have the same number of cakes with them. If the first child distributes his cakes to the remaining six children such that he doubles their respective number of cakes, then he will be left with four cakes. Instead, if the second child takes away two cakes from each of the remaining six children, then he will be left with three cakes less than the number of cakes that the first child initially had. What is the total number of cakes that are there with the third to the seventh child

Answer 1

Look at the question that Steve answered 3 years ago

http://www.jiskha.com/display.cgi?id=1372679603
It is identical to yours except there were 7 children instead of your 10
BUT, in your question it seems that they changed the 7 to 10 but failed to change the associated numbers.
I suspect a typo, if not , the question is confusing.

Answer 2

To solve this problem, let's break it down step by step:

1. Let's assume the first child initially had x number of cakes. Since they distributed cakes to the remaining six children and were left with four cakes, we can write the equation x - 6(y + 4) = 4, where y represents the number of cakes each remaining child received.

2. Simplifying the equation, we have x - 6y - 24 = 4.

3. Now let's consider the second child. They took away two cakes from each of the remaining six children, so the number of cakes left with the second child would be y - 2.

4. According to the problem, the second child would have three cakes less than the number of cakes the first child initially had. So we can write the equation y - 2 = x - 3.

5. Combining equations 3 and 4, we have y - 2 = x - 3 = x - 6y - 24.

6. Simplifying equation 5, we get x - 6y - 24 = y - 2.

7. Further simplifying, we have x - y = 22.

8. Since the first child distributed cakes to six remaining children, the total number of cakes is x + 6y.

9. Therefore, we have x - y + 6y = 22 + 6y.

10. Simplifying further, we get x + 5y = 22.

11. Now, considering the third to the seventh child, we need to find the total number of cakes they have. Let's assign variables a, b, c, d, and e to represent the number of cakes each child has, respectively.

12. We know that a + b + c + d + e = x + 6y.

13. Using equation 10, we can rewrite a + b + c + d + e = 22 + 6y.

So, the total number of cakes that the third to the seventh child have is 22 + 6y.