Question
\( 1 \leftarrow \) Complete parts a) and b). a) If \( 30 \% \) of a number is 60 , is the number greater than or less than 60 ? Explain. b) If \( 150 \% \) of a number is 60 , is the number greater than or less than 60 ? Explain.
Ask by Tran Hodges. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a) The number is greater than 60.
b) The number is less than 60.
Solution
a) Given that \( 30\% \) of a number \( x \) is 60, we write the equation as:
\[
0.30x = 60
\]
To solve for \( x \), divide both sides of the equation by \( 0.30 \):
\[
x = \frac{60}{0.30} = 200
\]
Since \( 200 > 60 \), the number is greater than 60.
b) Given that \( 150\% \) of a number \( x \) is 60, we write the equation as:
\[
1.50x = 60
\]
To solve for \( x \), divide both sides by \( 1.50 \):
\[
x = \frac{60}{1.50} = 40
\]
Since \( 40 < 60 \), the number is less than 60.
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Simplify this solution Bonus Knowledge
To tackle part a), we start with the equation derived from the statement: \( 0.30 \times x = 60 \). By solving for \( x \), we get \( x = \frac{60}{0.30} = 200 \). Hence, since 200 is greater than 60, we conclude that the number is greater than 60. For part b), we again set up an equation: \( 1.5 \times x = 60 \). Solving for \( x \) gives us \( x = \frac{60}{1.5} = 40 \). Since 40 is less than 60, we find that the number is less than 60.
