step by step solution. 30 increased by what part of itself gives 62?

We are given the statement: **30 increased by what part of itself gives 62?**

Let's break it down and solve it step by step.

### Step 1: Translate the word problem into an equation

Let \( x \) represent the "part of itself" that increases 30. The phrase **"30 increased by what part of itself"** translates to:

\[
30 + x \cdot 30 = 62
\]

Here, \( x \cdot 30 \) represents the part of 30 that we are looking for, and adding this part to 30 should give us 62.

### Step 2: Simplify the equation

Simplify the equation:

\[
30 + 30x = 62
\]

### Step 3: Solve for \( x \)

To solve for \( x \), subtract 30 from both sides:

\[
30x = 62 - 30
\]
\[
30x = 32
\]

Next, divide both sides by 30:

\[
x = \frac{32}{30}
\]

### Step 4: Simplify the fraction

Simplify the fraction:

\[
x = \frac{16}{15}
\]

### Step 5: Interpret the result

The part of 30 that increases it to 62 is \( \frac{16}{15} \) of itself. This means that 30 is increased by \( \frac{16}{15} \times 30 = 32 \), which gives the final result of 62.

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Here are 5 related questions for further practice:
1. What is 50 increased by what part of itself gives 75?
2. If 40 increased by a part of itself results in 64, what is the part?
3. How do you express "20 increased by what part of itself gives 45" as an equation?
4. Solve for \( x \): 35 increased by what part of itself gives 49.
5. What part of 25 needs to be added to it to get 55?

**Tip:** Always translate word problems into mathematical equations by carefully identifying keywords like "increased by" or "part of itself".

30 increased by what part of itself gives 62?

Find out how to solve the algebraic word problem '30 increased by what part of itself gives 62' with a detailed, step-by-step breakdown. Learn about solving linear equations and fraction simplification. Suitable for Grades 6-8 students.

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