Solving a Simple Algebraic Equation: What Number when Multiplied by 5 and Added 15 Gives 100?

Have you ever encountered a math problem where a specific number needs to be identified based on a set of operations? Let's explore a straightforward example: if a certain number is multiplied by 5 and then 15 is added, the result is 100. What is the number?

The Problem: What Number is It?

In this problem, you are given the following equation:

K × 5 15 100

Let's solve this problem step by step to find the value of K.

Step-by-Step Solution

Let the number be K.

Step 1: Simplify the Equation

K × 5 15 100

Subtract 15 from both sides of the equation:

5K 15 - 15 100 - 15

This simplifies to:

5K 85

Step 2: Solve for K

Divide both sides of the equation by 5:

5K / 5 85 / 5

This simplifies to:

K 17

Therefore, the number is 17.

Verification

To verify the solution, let's substitute K 17 back into the original equation:

17 × 5 15 85 15 100

Indeed, the result is 100, confirming that the solution is correct.

Alternative Methods

Here are a few alternative ways to solve the equation:

K × 5 15 100 K × 5 100 - 15 K × 5 85 K 85 / 5 K 17

Another approach is to work backward:

100 - 15 85

85 / 5 17

Both methods yield the same result, proving the solution is accurate.

Wrap-Up

Solving algebraic equations can be challenging at times, but with a systematic approach, it becomes much simpler. In this case, we identified that a number, when multiplied by 5 and then 15 is added, results in 100. Through basic algebraic manipulation, we found that the number is 17. This problem not only tests your arithmetic skills but also reinforces your understanding of basic algebra.

Feel free to practice more similar problems to enhance your problem-solving skills in mathematics. Happy calculating!