Question

12 mark for review the positive number a is 230% of the number b, and a is 60% of the number c. if c is p% of b, which of the following is closest to the value of p? a 138 b 217 c 283 d 383

Explanation:

Step1: Translate percentages to equations

Given \( a = 230\% \times b=\frac{230}{100}b = 2.3b \) and \( a = 60\% \times c=\frac{60}{100}c = 0.6c \).

Step2: Relate \( c \) and \( b \)

Since \( 2.3b=0.6c \), solve for \( c \) in terms of \( b \): \( c=\frac{2.3}{0.6}b \).

Step3: Find \( p\% \)

We know \( c = p\% \times b=\frac{p}{100}b \). So \( \frac{p}{100}=\frac{2.3}{0.6} \).
Calculate \( \frac{2.3}{0.6}\approx3.833\), then \( p = 3.833\times100\approx383.33 \)? Wait, no, wait: Wait, no, I made a mistake. Wait, \( a = 2.3b \) and \( a = 0.6c \), so \( 2.3b=0.6c \), so \( c=\frac{2.3}{0.6}b\approx3.833b \)? No, wait, no: Wait, no, if \( a = 230\% \) of \( b \), so \( a = 2.3b \), and \( a = 60\% \) of \( c \), so \( a = 0.6c \). So set equal: \( 2.3b=0.6c \), so \( c=\frac{2.3}{0.6}b \approx 3.833b \)? Wait, but that would mean \( c \) is \( 383.33\% \) of \( b \), so \( p\approx383 \)? But wait, no, wait, maybe I flipped. Wait, no: Let's re - check. If \( a = 2.3b \) and \( a = 0.6c \), then \( 0.6c=2.3b \), so \( c=\frac{2.3}{0.6}b\approx3.833b \), so \( c = 383.33\% \) of \( b \), so \( p\approx383 \)? But wait, the options have D as 383. Wait, but let's recalculate \( \frac{2.3}{0.6} \): \( 2.3\div0.6 = 3.833\cdots \), so \( p = 3.833\cdots\times100\approx383 \). Wait, but maybe I messed up the direction. Wait, no: \( a \) is 230% of \( b \) (so \( a \) is bigger than \( b \)), and \( a \) is 60% of \( c \) (so \( c \) is bigger than \( a \), hence \( c \) is much bigger than \( b \)). So \( c=\frac{a}{0.6}=\frac{2.3b}{0.6}\approx3.833b \), so \( c \) is \( 383.33\% \) of \( b \), so \( p\approx383 \), which is option D. Wait, but let's check again. Wait, 230% of \( b \) is \( a \), and \( a \) is 60% of \( c \), so \( c=\frac{a}{0.6}=\frac{2.3b}{0.6}\approx3.833b \), so \( c \) is \( 383.33\% \) of \( b \), so \( p\approx383 \), so the answer is D.
Wait, but wait, maybe I made a mistake in the percentage direction. Let's re - express:

\( a = 230\%b\implies a = 2.3b \)

\( a = 60\%c\implies a = 0.6c\implies c=\frac{a}{0.6} \)

Substitute \( a = 2.3b \) into \( c=\frac{a}{0.6} \): \( c=\frac{2.3b}{0.6}=\frac{23b}{6}\approx3.833b \)

Now, \( c = p\%b=\frac{p}{100}b \), so \( \frac{p}{100}=\frac{23}{6}\approx3.833 \)

Then \( p=\frac{23}{6}\times100=\frac{2300}{6}\approx383.33 \)

So \( p\approx383 \), which is option D.

Answer:

D. 383