Solving the Problem: If thrice a number is increased by 11, the result is 35. What is the number?

Math problems can be a fun challenge, and sometimes they become interesting when they involve simple algebraic equations. One such problem is: if thrice a number increased by 11 gives a result of 35, what is the number?

Understanding the Problem

To tackle this problem, we first need to understand what the problem is asking. We are looking for a number, and we know that if we triple this number and then add 11, we get 35. Let's denote this unknown number by x.

Formulating the Equation

We can express the given information in a mathematical equation. The equation is:

3x 11 35

This equation states that three times the number (3x) plus 11 equals 35.

Solving the Equation

Now, let's solve this equation step-by-step.

Subtraction Step

We start by isolating the term with x on one side of the equation. To do this, we subtract 11 from both sides of the equation:

3x 35 - 11

3x 24

This step helps us eliminate the constant term on the left side of the equation.

Division Step

Next, we divide both sides of the equation by 3 to isolate x:

x frac{24}{3}

x 8

This final step gives us the value of the unknown number, which is 8.

Verifying the Solution

To ensure our solution is correct, we can substitute the value of x back into the original equation:

3(8) 11 35

24 11 35

35 35

The equation holds true, confirming that our solution is correct.

Alternative Methods and Additional Insights

Some readers might approach this problem differently, such as:

Working Backwards

Others might prefer to work backwards. Starting with 35, we subtract 11 to get 24, and then divide 24 by 3 to get 8:

35 - 11 24

24 3x

8 x

This method also leads to the same solution.

Reverse Operations

Another approach is to think of the inverse operations. Adding 11 to a number and then multiplying by 3 to get 35 means the reverse operations would be to divide 35 by 3 and then subtract 11:

35 / 3 11.666... (approx 11.67)

11.666... - 11 0.666... (approx 0.67)

This method is less conventional but can be used to verify the correctness of the solution.

Conclusion

In conclusion, the number that satisfies the given condition is 8. Whether through algebraic manipulation or working backwards, the solution remains consistent. Understanding how to set up and solve such equations is an essential skill in algebra and can be applied to more complex problems in the future.