If $30 \%$ of a number is $84$ and $70 \%$ of the same number is $196$ , find $40 \%$ of that number. $\newline$ Answer:

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Grade 8

Experimental probability

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Q. If

30 \%

of a number is

84

and

70 \%

of the same number is

196

, find

40 \%

of that number.

\newline

Answer:

Define Unknown Number: Let's denote the unknown number as $x$ . We are given that $30\%$ of $x$ is $84$ . We can express this as an equation: $\newline$ $0.30 \times x = 84$ $\newline$ Now, we need to solve for $x$ .
Equation Setup: Divide both sides of the equation by $0.30$ to isolate $x$ : $\newline$ $x = \frac{84}{0.30}$ $\newline$ Calculate the value of $x$ .
Isolate and Solve for x: Performing the division gives us: $\newline$ $x = 280$ $\newline$ Now we have found the value of the whole number.
Verify Calculation: We are also given that $70\%$ of $x$ is $196$ , which we can use to verify our calculation of $x$ . Let's check this with an equation: $\newline$ $0.70 \times x = 196$ $\newline$ Substitute the value of $x$ we found into this equation to see if it holds true.
Calculate $40\%$ of $x$ : Substituting $x = 280$ into the equation gives us: $\newline$ $0.70 \times 280 = 196$ $\newline$ Calculate the result to verify.
Calculate $40$ \% of $x$ : Substituting $x = 280$ into the equation gives us: $\newline$ $0.70 \times 280 = 196$ $\newline$ Calculate the result to verify.Performing the multiplication gives us: $\newline$ $196 = 196$ $\newline$ This confirms that our value for $x$ is correct since both sides of the equation are equal.
Calculate $40$ % of x: Substituting $x = 280$ into the equation gives us: $\newline$ $0.70 \times 280 = 196$ $\newline$ Calculate the result to verify.Performing the multiplication gives us: $\newline$ $196 = 196$ $\newline$ This confirms that our value for $x$ is correct since both sides of the equation are equal.Now we need to find $40$ % of $x$ . We can express this as: $\newline$ $0.40 \times x$ $\newline$ Substitute the value of $x$ we found into this expression.
Calculate $40$ % of x: Substituting $x = 280$ into the equation gives us: $\newline$ $0.70 \times 280 = 196$ $\newline$ Calculate the result to verify.Performing the multiplication gives us: $\newline$ $196 = 196$ $\newline$ This confirms that our value for $x$ is correct since both sides of the equation are equal.Now we need to find $40$ % of $x$ . We can express this as: $\newline$ $0.40 \times x$ $\newline$ Substitute the value of $x$ we found into this expression.Substituting $x = 280$ into the expression gives us: $\newline$ $0.40 \times 280$ $\newline$ Calculate the result to find $40$ % of the number.
Calculate $40$ % of $x$ : Substituting $x = 280$ into the equation gives us: $\newline$ $0.70 \times 280 = 196$ $\newline$ Calculate the result to verify.Performing the multiplication gives us: $\newline$ $196 = 196$ $\newline$ This confirms that our value for $x$ is correct since both sides of the equation are equal.Now we need to find $40$ % of $x$ . We can express this as: $\newline$ $0.40 \times x$ $\newline$ Substitute the value of $x$ we found into this expression.Substituting $x = 280$ into the expression gives us: $\newline$ $0.40 \times 280$ $\newline$ Calculate the result to find $40$ % of the number.Performing the multiplication gives us: $\newline$ $x = 280$ $0$ $\newline$ So, $40$ % of the number is $x = 280$ $0$ .