the positive number r is 133.7% of the positive number s, and s is p% of r. which of the following is…

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\neq0 )). 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