# Solving for $k$: Digit Product = $\dfrac{25k}{8}-211$

• MHB
• anemone
In summary, "solving for k" means finding the value of the variable k that satisfies an equation. To solve for k, algebraic techniques are used to isolate the variable and find its specific value. The purpose of solving for k is to find a specific value that can be used to solve related problems or verify the accuracy of the equation. There may be restrictions on the possible values of k, depending on the context of the problem. It is important to consider these restrictions when solving for k. To check the solution for k, it can be substituted back into the original equation and if both sides are equal, the solution is correct. It is always recommended to check solutions for accuracy.
anemone
Gold Member
MHB
POTW Director
Find all positive integers $k$ such that the product of the digits of $k$, in the decimal system, equals $\dfrac{25k}{8}-211$.

72 and 88

## 1. What is the purpose of solving for $k$ in this equation?

The purpose of solving for $k$ in this equation is to find the value of the variable that makes the equation true. In other words, it is the value of $k$ that satisfies the equation and makes the digit product on one side equal to the fraction on the other side minus 211.

## 2. How do you solve for $k$ in this equation?

To solve for $k$, you can use algebraic methods such as combining like terms, isolating the variable, and using inverse operations. You can also use a calculator or computer program to find the numerical value of $k$.

## 3. What is the significance of the digit product in this equation?

The digit product in this equation represents the product of all the digits in a number. In this case, it is the product of the digits in $k$. This is important because it allows us to represent a large number with fewer digits and makes the equation more manageable.

## 4. Can this equation have multiple solutions for $k$?

Yes, this equation can have multiple solutions for $k$. This means that there can be more than one value of $k$ that satisfies the equation and makes the digit product equal to the fraction minus 211. However, some solutions may not be valid in certain contexts or may be more practical than others.

## 5. What are some real-world applications of solving for $k$ in this equation?

Solving for $k$ in this equation can be useful in various mathematical and scientific contexts. For example, it can be used to solve problems related to digit products, fractions, and equations. It can also be applied in fields such as finance, engineering, and computer science to calculate values or make predictions based on given data.

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