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Of a squirrel's hidden nuts, for every   that get found, there are   that do not get found. A squirrel hid   nuts all together.

Question

Of a squirrel's hidden nuts, for every

  • that get found, there are
  • that do not get found.

A squirrel hid

  • nuts all together.
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Solution

To answer the question about the hidden nuts of the squirrel, let’s work through the problem systematically.

  1. Break Down the Problem

    • Let x x represent the number of nuts that get found.
    • For every a a nuts found, there are b b nuts that do not get found.
    • This means that for every a+b a + b total nuts hidden, a a are found and b b are not found.
    • If "a squirrel hid N N nuts altogether", we can express this relationship mathematically.
  2. Relevant Concepts

    • We can represent the total number of hidden nuts N N as: N=x+(bax) N = x + \left(\frac{b}{a} x\right)
    • Here, bax \frac{b}{a} x represents the number of nuts that do not get found.
  3. Analysis and Detail

    • We can rewrite this equation based on the ratio of nuts:
      • Let k=ba k = \frac{b}{a} , then we can express the equation as: N=x+kx=x(1+k) N = x + kx = x(1 + k)
    • Therefore, by isolating x x : x=N1+k x = \frac{N}{1 + k}
    • The nuts that do not get found can then be computed as:
      • (1+k)xx=kx(1 + k)x - x = kx
  4. Verify and Summarize

    • Check that the value of x x makes sense with the total N N .
    • If a a and b b are specified, we can calculate k k , then find how many nuts were found and how many were not found.

Final Answer

If we know specific values for a a , b b , and N N , we can compute the total nuts found and not found using the formulas derived. Please provide the specific values for a a , b b , and N N to perform the calculations.

This problem has been solved

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