Question

In martin’s class of 20 students, 4 students report that social studies is their favorite class and 75% of the Students report that PE is their favorite class. Show your work to explain how to determine whether more students prefer social studies or PE. This needs to be written in an expression

Answer 1

4/20 students say S.S. is their favorite
75% say PE is their favorite
you need to get them in the same conditions, one is fraction, and one is percent
4/20= ?%    /100  4        __   cross multiply on paper
                            20     100
4x100= 400/20=20
20% say s.s. is their favorite
20% is smaller than 75%
expresson: 4
                  20< 75%

Answer 2

Well, we know the total amount of students in the class is 20.  4 of them prefer SS, and 75% of them prefer PE.

now, if we take 20 to be the 100%, what is 4 off of it in percentage?

$\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 20&100\\ 4&p \end{array}\implies \cfrac{20}{4}=\cfrac{100}{p}\implies p=\cfrac{4\cdot 100}{20}\implies p=\stackrel{\%}{20}$

so, we know 20% prefer SS, and 75% prefer PE, well, notice the percentages, is clear that 20% < 75%

if we make the total class say hmmm "x", then 20% of x is (20/100) * x, or 0.2x, and 75% of x is (75/100) * x, or 0.75x, thus

$\bf \stackrel{\textit{social studies}}{0.2x}\ \textless \ \stackrel{\textit{physical education}}{0.75x}$