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If
30% of a number is 78 and
20% of the same number is 52 , find
50% of that number.
Answer:

If $30 \%$ of a number is $78$ and $20 \%$ of the same number is $52$ , find $50 \%$ of that number. $\newline$ Answer:

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Find the total given a part and a percent

Full solution

Q. If

30 \%

of a number is

78

and

20 \%

of the same number is

52

, find

50 \%

of that number.

\newline

Answer:

Determine Value of $30$ %: Determine the value of $30$ % of the number. $\newline$ We are given that $30$ % of the number is $78$ . $\newline$ This can be represented by the equation $0.30 \times \text{number} = 78$ . $\newline$ To find the number, we divide $78$ by $0$ . $30$ . $\newline$ Calculation: $\text{number} = \frac{78}{0.30}$
Calculate Number: Calculate the number based on the $30\%$ value. $\newline$ Calculation: $\text{number} = \frac{78}{0.30} = 260$
Verify with $20$ %: Verify the calculation with the $20$ % information. $\newline$ We are given that $20\%$ of the number is $52$ . $\newline$ This can be represented by the equation $0.20 \times \text{number} = 52$ . $\newline$ To verify, we check if $20\%$ of $260$ is indeed $52$ . $\newline$ Calculation: $0.20 \times 260 = 52$
Calculate $50$ %: Calculate $50\%$ of the number. $\newline$ Now that we have verified the number is $260$ , we can find $50\%$ of it. $\newline$ $50\%$ of the number is the same as dividing the number by $2$ . $\newline$ Calculation: $50\%$ of number $= 260 / 2$
Determine Final Answer: Determine the final answer. $\newline$ Calculation: $50\%$ of number $= 260 / 2 = 130$

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