91Ó°ÊÓ

Use the following system of equations.

$x+y+z=5$

$z=2y$

$3.2x+2.4y+4z=16.80$

Apply the Cramer’s rule for the value of x.

$x=\frac{\left|\begin{array}{ccc}j& b& c\\ k& e& f\\ l& h& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$

Use the equations and substitute the value of a, b, c, d, e, f, g, h, i, j, k and l into role="math" localid="1647272330795" $x=\frac{\left|\begin{array}{ccc}j& b& c\\ k& e& f\\ l& h& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of determinants to write the value of x.

$\begin{array}{c}x=\frac{\left|\begin{array}{ccc}5& 1& 1\\ 0& −2& 1\\ 16.8& 2.4& 4\end{array}\right|}{\left|\begin{array}{ccc}1& 1& 1\\ 0& −2& 1\\ 3.2& 2.4& 4\end{array}\right|}\\ =\frac{−\frac{8}{5}}{−\frac{4}{5}}\\ =2\end{array}$

Apply the Cramer’s rule for the value of y.

$y=\frac{\left|\begin{array}{ccc}a& j& c\\ d& k& f\\ g& l& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$

Use the equations and substitute the value of a, b, c, d, e, f, g, h, i, j, k and l intorole="math" localid="1647272524741" $y=\frac{\left|\begin{array}{ccc}a& j& c\\ d& k& f\\ g& l& i\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of determinants to write the value of y.

$\begin{array}{c}y=\frac{\left|\begin{array}{ccc}1& 5& 1\\ 0& 0& 1\\ 3.2& 16.8& 4\end{array}\right|}{\left|\begin{array}{ccc}1& 1& 1\\ 0& −2& 1\\ 3.2& 2.4& 4\end{array}\right|}\\ =\frac{−\frac{4}{5}}{−\frac{4}{5}}\\ =1\end{array}$

Apply the Cramer’s rule for the value of z.

$z=\frac{\left|\begin{array}{ccc}a& b& j\\ d& e& k\\ g& h& l\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$

Use the equations and substitute the value of a, b, c, d, e, f, g, h, i, j, k and l into role="math" localid="1647272661781" $z=\frac{\left|\begin{array}{ccc}a& b& j\\ d& e& k\\ g& h& l\end{array}\right|}{\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|}$after it perform simplification of determinants to write the value of z.

$\begin{array}{c}z=\frac{\left|\begin{array}{ccc}1& 1& 5\\ 0& −2& 0\\ 3.2& 2.4& 16.8\end{array}\right|}{\left|\begin{array}{ccc}1& 1& 1\\ 0& −2& 1\\ 3.2& 2.4& 4\end{array}\right|}\\ =\frac{−\frac{8}{5}}{−\frac{4}{5}}\\ =2\end{array}$

The obtained value of x is 2, y is 1 and z is 2 so the amount of peanuts is 2 pounds, amount of raisins is 1 pound and carob-coated pretzels is 2 pounds.