Question

Let \[R = gS - 4\], when \[S = 8\], the value of \[R = 16\]. When \[S = 10\], what is the value of \[R\]?

Answer 1

Hint: As given in the question, the given equation \[R = gS - 4\] has three unknown variables. All the three variables are interrelated to each other. Also given, if S=8 then R will be 16. Hence, to find out the value of R when S=10, we need to find out the value of remaining unknown.

Complete step-by-step solution:
As per the question, among three unknown variables, values of two unknown variables are given and we need to find out the remaining one for further solution of the given question.
So, given in the question,
When value of \[S = 8\], value of \[R = 16\]. So, we will put the value of \[S\] and \[R\] here, and we get:
\[ \Rightarrow g \times 8 - 4 = 16\]
Here the remaining unknown is going. So, we need to find out the value of \[g\]:
\[ \Rightarrow g \times 8 = 20\]
\[ \Rightarrow g = \dfrac{{20}}{8}\]
Now for another part of the question, values of two unknowns are now known:
\[S = 10\]and \[g = \dfrac{{20}}{8}\]
Now, as per the question we need to find out the value of R.
Given equation is \[R = gS - 4\] where \[g\] and \[S\] are known. So, we will put the values of \[g\] and \[S\], and we get:
\[ \Rightarrow \dfrac{{20}}{8} \times 10 - 4 = R\]
\[ \Rightarrow \dfrac{{200}}{8} - 4 = R\]
\[ \Rightarrow 25 - 4 = R\]
\[ \Rightarrow R = 21\]
\[ \Rightarrow \] Therefore, the value of \[R = 21\].

Note: This type of question generally comes with more than one unknown. But the question always comes with sufficient data that you always have to find out only one unknown. If the question further proceeds, then you have to find out solutions by using previous data that you have already obtained in the first part.