Chapter 9.5, Problem 27PPS

To determine

Find the solution.

Answer to Problem 27PPS

  $t=30$ or $t=40$ days after stock purchased

Explanation of Solution

Given Information: $p=3.5t-0.05t^2$ and $p=\$60$

Formula Used: $a^2-2ab+b^2={(a-b)}^2$ and $a^2-b^2=(a+b)(a-b)$

Calculation:

  $p=3.5t-0.05t^2$

As, $p=\$60$

  $60=3.5t-0.05t^2$

Now, simplify

  $0.05t^2-3.5t+60=0$

Now, to make coefficient of $t^2$ = 1, multiply the equation by 20.

  $t^2-70t+1200=0$

Now, adding & subtracting the square of half the coefficient of t.

  $t^2-70t+1200+{\left(\frac{70}{2}\right)}^2-{\left(\frac{70}{2}\right)}^2=0$

Now use formula, $a^2-2ab+b^2={(a-b)}^2$

  ${\left(t-35\right)}^2+1200-{35}^2=0$

So,

  ${\left(t-35\right)}^2+1200-1225=0$

So,

  ${\left(t-35\right)}^2-25=0$

Now, square root of 25 is 5

  ${\left(t-35\right)}^2-{\left(5\right)}^2=0$

Now use formula, $a^2-b^2=(a+b)(a-b)$

  $\left(t-35+5\right)\left(t-35-5\right)=0$

Now,

  $\left(t-30\right)\left(t-40\right)=0$

Hence,

  $t=30$ or $t=40$ days after stock purchased