Answer:
System of Equations
[tex]\large \begin{cases}P(x)=-x^2+7x+10\\Q(x)= 4x\end{cases}[/tex]
Use the substitution method to solve the given system of equations:
[tex]\large\begin{aligned}P(x) & = Q(x)\\-x^2+7x+10 & = 4x\\-x^2+7x+10 - 4x & = 0\\-x^2+3x+10 & = 0\\x^2-3x-10 & = 0\\x^2-5x+2x-10 & = 0\\x(x-5)+2(x-5) & = 0\\(x+2)(x-5) & = 0\\\implies x+2 & = 0 \implies x=-2\\\implies x-5 & = 0 \implies x=5\end{aligned}[/tex]
As [tex]x[/tex] represents the number of days, then [tex]x\geq 0[/tex]
Therefore:
- The viable answer is when [tex]x=5[/tex] → 5 days
- The non-viable answer is when [tex]x=-2[/tex] (as the number of days cannot be negative)
So the two students will earn the same profit after 5 days.
