Question

the positive number r is 133.7% of the positive number s, and s is p% of r. which of the following is closest to the value of p?
(a) 33.7
(b) 66.9
(c) 74.8
(d) 133.7

Explanation:

Step1: Translate the problem into equations

We know that \( r \) is \( 133.7\% \) of \( s \), so mathematically, this can be written as \( r = 1.337s \) (since \( 133.7\% = 1.337 \) in decimal form). Also, \( s \) is \( p\% \) of \( r \), which translates to \( s=\frac{p}{100}r \) (since \( p\%=\frac{p}{100} \)).

Step2: Substitute \( r \) from the first equation into the second equation

Substitute \( r = 1.337s \) into \( s=\frac{p}{100}r \). We get \( s=\frac{p}{100}(1.337s) \). Since \( s \) is a positive number, we can divide both sides of the equation by \( s \) (because \( s
eq0 \)). So, dividing both sides by \( s \) gives \( 1=\frac{p}{100}(1.337) \).

Step3: Solve for \( p \)

Now, we solve the equation \( 1 = \frac{1.337p}{100} \) for \( p \). First, multiply both sides of the equation by \( 100 \) to get \( 100=1.337p \). Then, divide both sides by \( 1.337 \) to find \( p \). So, \( p=\frac{100}{1.337}\approx74.8 \).

Answer:

C. 74.8