Chapter 9.5, Problem 4GP

To determine

Find the solution.

Answer to Problem 4GP

66 jerseys

Explanation of Solution

Given Information: $\$620$

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

Calculation:

  $0.1x^2+2.4x+25=620$

Now, to make coefficient of $x^2$ = 1, multiply the equation by 10.

  $x^2+24x+250=6200$

So,

  $x^2+24x+250-6200=0$

Now, simplify

  $x^2+24x-5950=0$

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

  $x^2+24x-5950+{\left(\frac{24}{2}\right)}^2-{\left(\frac{24}{2}\right)}^2=0$

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

  ${\left(x+12\right)}^2-5950-{12}^2=0$

So,

  ${\left(x+12\right)}^2-5950-144=0$

So,

  ${\left(x+12\right)}^2-6094=0$

Now, square root of 6094 is 78

  ${\left(x+12\right)}^2-{\left(78\right)}^2=0$

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

  $\left(x+12+78\right)\left(x+12-78\right)=0$

Now,

  $\left(x+90\right)\left(x-66\right)=0$

Hence,

  $x=-99$ or $x=66$ jerseys