Question

Use the​ five-step strategy for solving word problems to find the number described.
When 40​% of a number is added to the​ number, the result is 182.
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Part 1
What is the​ number?

Answer 1

To solve the problem using the five-step strategy, let's follow the steps:

### Step 1: Understand the problem
We need to find a number such that when 40% of that number is added back to the number itself, the total equals 182.

### Step 2: Translate the problem into a mathematical expression
Let \( x \) be the number we want to find. According to the problem, we can express the relationship as:
\[
x + 0.4x = 182
\]

### Step 3: Solve the equation
Combine like terms:
\[
1x + 0.4x = 1.4x
\]
So we have:
\[
1.4x = 182
\]

Now, divide both sides by 1.4 to solve for \( x \):
\[
x = \frac{182}{1.4}
\]

Calculating this gives:
\[
x = 130
\]

### Step 4: Check the solution
Now, let’s check if our solution makes sense:
- 40% of 130 is:
\[
0.4 \times 130 = 52
\]
- Adding this to the original number:
\[
130 + 52 = 182
\]
This confirms our solution is correct.

### Step 5: State the answer
The number is \( \boxed{130} \).