91Ó°ÊÓ

If a container of liquid contains 60 oz of solution, what is the number of ounces of pure acid if the given solution contains the following acid concentrations? (a) \(10 \%\) (b) \(25 \%\) (c) \(40 \%\) (d) \(50 \%\)

Complete each statement. If solving a system leads to a false statement such as \(0=3,\) the solution set is _____________.

LeBron and Jose measured a basketball court and found that the width of the court was \(44 \mathrm{ft}\) less than the length. If the perimeter was \(288 \mathrm{ft}\), what were the length and the width of the basketball court?

Determine whether the given ordered pair is a solution of the given system. $$ \begin{array}{l} 2 x-y=8 \\ 3 x+2 y=20 \end{array} ; \quad(5,2) $$

How many gallons each of \(25 \%\) alcohol and \(35 \%\) alcohol should be mixed to obtain 20 gal of \(32 \%\) alcohol? $$ \begin{array}{|c|c|c|} \hline \begin{array}{c} \text { Gallons } \\ \text { of Solution } \end{array} & \begin{array}{c} \text { Percent } \\ \text { (as a decimal) } \end{array} & \begin{array}{c} \text { Gallons of } \\ \text { Pure Alcohol } \end{array} \\ \hline x & 25 \%=0.25 & \\ y & 35 \%=0.35 & \\ 20 & 32 \%= & \\ \hline \end{array} $$

A party mix is made by adding nuts that sell for \(\$ 2.50\) per \(\mathrm{kg}\) to a cereal mixture that sells for \(\$ 1\) per \(\mathrm{kg} .\) How much of each should be added to obtain \(30 \mathrm{~kg}\) of a mix that will sell for \(\$ 1.70\) per \(\mathrm{kg}\) ? $$ \begin{array}{|l|c|c|c|} \hline & \begin{array}{c} \text { Number of } \\ \text { Kilograms } \end{array} & \begin{array}{c} \text { Price per } \\ \text { Kilogram } \\ \text { (in dollars) } \end{array} & \begin{array}{c} \text { Value } \\ \text { (in } \\ \text { dollars) } \end{array} \\ \text { Nuts } & x & 2.50 & \\ \text { Cereal } & y & 1.00 & \\ \text { Mixture } & & 1.70 & \\ \hline \end{array} $$

Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. $$ \begin{array}{l} 5 x-4 y=9 \\ 3-2 y=-x \end{array} $$

Solve each system. $$\begin{array}{l}4 x-z=-6 \\\\\frac{3}{5} y+\frac{1}{2} z=0 \\\\\frac{1}{3} x+\frac{2}{3} z=-5\end{array}$$

A motor scooter travels 20 mi in the same time that a bicycle travels \(8 \mathrm{mi}\). If the rate of the scooter is 5 mph more than twice the rate of the bicycle, find both rates.

Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. $$ \begin{array}{l} y=0.5 x \\ 1.5 x-0.5 y=5.0 \end{array} $$