Understanding the Number Problem

The question asks us to find a specific unknown number. We are given a condition involving this number: if we take 70% of it and then subtract 70, the result we get is exactly 70.

Setting up the Algebraic Equation

Let's represent the unknown number with a variable, say '$x$'.

• 70% of the number can be written as $70\%$ of $x$, which is $\frac{70}{100} \times x$ or $0.70x$.
• The question states that 70 is subtracted from this amount. So, we have the expression: $0.70x - 70$.
• We are told that the remainder (the result of this subtraction) is 70.

Therefore, we can set up the following equation:

$$ 0.70x - 70 = 70 $$

Solving for the Number 'x'

Now, we need to solve this equation to find the value of '$x$'.

1. Isolate the term with '$x$': Add 70 to both sides of the equation to move the constant term to the right side. $$ 0.70x - 70 + 70 = 70 + 70 $$ $$ 0.70x = 140 $$
2. Solve for '$x$': Divide both sides by 0.70 to find the value of the number '$x$'. $$ x = \frac{140}{0.70} $$ To make the division easier, we can multiply the numerator and denominator by 10: $$ x = \frac{140 \times 10}{0.70 \times 10} $$ $$ x = \frac{1400}{7} $$ $$ x = 200 $$

Verifying the Solution

Let's check if our answer '$x = 200$' satisfies the original condition:

• Calculate 70% of 200: $$ 0.70 \times 200 = 140 $$
• Subtract 70 from the result: $$ 140 - 70 = 70 $$

The remainder is indeed 70, which matches the condition given in the question. Thus, the number is 200.

Analyzing the Options

The options provided were:

Our calculated value for the number is 200, which corresponds to option 1.