Chapter 5

In the following exercises, translate to a system of equations and solve. The difference of two complementary angles is 55 degrees. Find the measures of the angles.

In the following exercises, translate to a system of equations and solve. The difference of two complementary angles is 17 degrees. Find the measures of the angles.

In the following exercises, translate to a system of equations and solve. Two angles are supplementary. The measure of the larger angle is four more than three times the measure of the smaller angle. Find the measures of both angles.

In the following exercises, translate to a system of equations and solve. Two angles are supplementary. The measure of the larger angle is five less than four times the measure of the smaller angle. Find the measures of both angles.

In the following exercises, translate to a system of equations and solve. Two angles are complementary. The measure of the larger angle is twelve less than twice the measure of the smaller angle. Find the measures of both angles.

In the following exercises, translate to a system of equations and solve. Two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle. Find the measures of both angles.

In the following exercises, translate to a system of equations and solve. Wayne is hanging a string of lights 45 feet long around the three sides of his rectangular patio, which is adjacent to his house. The length of his patio, the side along the house, is five feet longer than twice its width. Find the length and width of the patio.

In the following exercises, translate to a system of equations and solve. Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that enclose his rectangular front yard. The length, the side along the house, is five feet less than three times the width. Find the length and width of the fencing.

In the following exercises, translate to a system of equations and solve. A frame around a rectangular family portrait has a perimeter of 60 inches. The length is fifteen less than twice the width. Find the length and width of the frame.

In the following exercises, translate to a system of equations and solve. The perimeter of a rectangular toddler play area is 100 feet. The length is ten more than three times the width. Find the length and width of the play area.

Sarah left Minneapolis heading east on the interstate at a speed of \(60 \mathrm{mph}\). Her sister followed her on the same route, leaving two hours later and driving at a rate of \(70 \mathrm{mph}\). How long will it take for Sarah's sister to catch up to Sarah?

College roommates John and David were driving home to the same town for the holidays. John drove \(55 \mathrm{mph},\) and David, who left an hour later, drove 60 mph. How long will it take for David to catch up to John?

At the end of spring break, Lucy left the beach and drove back towards home, driving at a rate of 40 mph. Lucy's friend left the beach for home 30 minutes (half an hour) later, and drove 50 mph. How long did it take Lucy's friend to catch up to Lucy?

Felecia left her home to visit her daughter driving \(45 \mathrm{mph}\). Her husband waited for the dog sitter to arrive and left home twenty minutes \((1 / 3\) hour) later. He drove 55 mph to catch up to Felecia. How long before he reaches her?

The Jones family took a 12 mile canoe ride down the Indian River in two hours. After lunch, the return trip back up the river took three hours. Find the rate of the canoe in still water and the rate of the current.

A motor boat travels 60 miles down a river in three hours but takes five hours to return upstream. Find the rate of the boat in still water and the rate of the current.

A motor boat traveled 18 miles down a river in two hours but going back upstream, it took 4.5 hours due to the current. Find the rate of the motor boat in still water and the rate of the current.

A river cruise boat sailed 80 miles down the Mississippi River for four hours. It took five hours to return. Find the rate of the cruise boat in still water and the rate of the current.

a small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

A small jet can fly 1,435 miles in 5 hours with a tailwind but only 1215 miles in 5 hours into \(a\) headwind. Find the speed of the jet in still air and the speed of the wind.

A commercial jet can fly 868 miles in 2 hours with a tailwind but only 792 miles in 2 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

A commercial jet can fly 1,320 miles in 3 hours with a tailwind but only 1,170 miles in 3 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

At a school concert, 425 tickets were sold. Student tickets cost \(\$ 5\) each and adult tickets cost \(\$ 8\) each. The total receipts for the concert were \(\$ 2,851\). Solve the system \(\left\\{\begin{array}{l}s+a=425 \\ 5 s+8 a=2,851\end{array}\right.\) to find \(s,\) the number of student tickets and \(a,\) the number of adult tickets.

The first graders at one school went on a field trip to the zoo. The total number of children and adults who went on the field trip was 115 . The number of adults was \(\frac{1}{4}\) the number of children. Solve the system $$ \left\\{\begin{array}{l} c+a=115 \\ a=\frac{1}{4} c \end{array}\right. $$ to find \(c,\) the number of children and \(a,\) the number of adults.

In the following exercises, translate to a system of equations and solve. Tickets to a Broadway show cost \(\$ 35\) for adults and \(\$ 15\) for children. The total receipts for 1650 tickets at one performance were \(\$ 47,150\). How many adult and how many child tickets were sold?

In the following exercises, translate to a system of equations and solve. Tickets for a show are \(\$ 70\) for adults and \(\$ 50\) for children. One evening performance had a total of 300 tickets sold and the receipts totaled \$17,200. How many adult and how many child tickets were sold?

In the following exercises, translate to a system of equations and solve. Tickets for a train cost \(\$ 10\) for children and \(\$ 22\) for adults. Josie paid \(\$ 1,200\) for a total of 72 tickets. How many children's tickets and how many adult tickets did Josie buy?

In the following exercises, translate to a system of equations and solve. Tickets for a baseball game are \(\$ 69\) for Main Level seats and \(\$ 39\) for Terrace Level seats. A group of sixteen friends went to the game and spent a total of \(\$ 804\) for the tickets. How many of Main Level and how many Terrace Level tickets did they buy?

In the following exercises, translate to a system of equations and solve. Tickets for a dance recital cost \(\$ 15\) for adults and \(\$ 7\) for children. The dance company sold 253 tickets and the total receipts were \(\$ 2,771\). How many adult tickets and how many child tickets were sold?

In the following exercises, translate to a system of equations and solve. Tickets for the community fair cost \(\$ 12\) for adults and \(\$ 5\) dollars for children. On the first day of the fair, 312 tickets were sold for a total of \(\$ 2,204 .\) How many adult tickets and how many child tickets were sold?

In the following exercises, translate to a system of equations and solve. Brandon has a cup of quarters and dimes with a total value of \(\$ 3.80\). The number of quarters is four less than twice the number of dimes. How many quarters and how many dimes does Brandon have?

In the following exercises, translate to a system of equations and solve. Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is \(\$ 0.95\). The number of nickels is two less than five times the number of dimes. How many nickels and how many dimes are in the coin purse?

In the following exercises, translate to a system of equations and solve. Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value \(\$ 13.10\). The number of quarters was fifteen more than three times the number of dimes. How many quarters and how many dimes did Peter have?

In the following exercises, translate to a system of equations and solve. Lucinda had a pocketful of dimes and quarters with a value of \(\$ \$ 6.20\). The number of dimes is eighteen more than three times the number of quarters. How many dimes and how many quarters does Lucinda have?

In the following exercises, translate to a system of equations and solve. A cashier has 30 bills, all of which are \(\$ 10\) or \(\$ 20\) bills. The total value of the money is \(\$ 460\). How many of each type of bill does the cashier have?

In the following exercises, translate to a system of equations and solve. A cashier has 54 bills, all of which are \(\$ 10\) or \(\$ 20\) bills. The total value of the money is \(\$ 910\). How many of each type of bill does the cashier have?

In the following exercises, translate to a system of equations and solve. Marissa wants to blend candy selling for \(\$ 1.80\) per pound with candy costing \(\$ 1.20\) per pound to get a mixture that costs her \(\$ 1.40\) per pound to make. She wants to make 90 pounds of the candy blend. How many pounds of each type of candy should she use?

In the following exercises, translate to a system of equations and solve. How many pounds of nuts selling for \(\$ 6\) per pound and raisins selling for \(\$ 3\) per pound should Kurt combine to obtain 120 pounds of trail mix that cost him \(\$ 5\) per pound?

In the following exercises, translate to a system of equations and solve. Hannah has to make twentyfive gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is \(\$ 1.79\) per gallon and the cost of the fruit drink is \(\$ 2.49\) per gallon. Hannah's budget requires that the punch cost \(\$ 2.21\) per gallon. How many gallons of soda and how many gallons of fruit drink does she need?

Joseph would like to make 12 pounds of a coffee blend at a cost of \(\$ 6.25\) per pound. He blends Ground Chicory at \(\$ 4.40\) a pound with Jamaican Blue Mountain at \(\$ 8.84\) per pound. How much of each type of coffee should he use?

Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost \(\$ 7.80\) per pound with French Roast Columbian coffee that cost \(\$ 8.10\) per pound to make a 20 pound blend. Their blend should cost them \(\$ 7.92\) per pound. How much of each type of coffee should they buy?

Jotham needs 70 liters of a \(50 \%\) alcohol solution. He has a \(\begin{array}{lllll}30 \% & \text { and an } & 80 \% & \text { solution }\end{array}\) available. How many liters of the \(30 \%\) and how many liters of the \(80 \%\) solutions should he mix to make the \(50 \%\) solution?

Joy is preparing 15 liters of a \(25 \%\) saline solution. She only has \(40 \%\) and \(10 \%\) solution in her lab. How many liters of the \(40 \%\) and how many liters of the \(10 \%\) should she mix to make the \(25 \%\) solution?

A scientist needs 65 liters of a \(15 \%\) alcohol solution. She has available a \(25 \%\) and a \(12 \%\) solution. How many liters of the \(25 \%\) and how many liters of the \(12 \%\) solutions should she mix to make the \(15 \%\) solution?

A scientist needs 120 liters of \(\begin{array}{lllll} & 20 \% & \text { acid solution for an }\end{array}\) experiment. The lab has available a \(25 \%\) and a \(10 \%\) solution. How many liters of the \(25 \%\) and how many liters of the \(10 \%\) solutions should the scientist mix to make the \(20 \%\) solution?

A \(90 \%\) antifreeze solution is to be mixed with a \(75 \%\) antifreeze solution to get 360 liters of a \(85 \%\) solution. How many liters of the \(90 \%\) and how many liters of the \(75 \%\) solutions will be used?

Hattie had \(\$ 3,000\) to invest and wants to earn \(10.6 \%\) interest per year. She will put some of the money into an account that earns \(12 \%\) per year and the rest into an account that earns \(10 \%\) per year. How much money should she put into each account?

Carol invested \(\$ 2,560\) into two accounts. One account paid \(8 \%\) interest and the other paid \(6 \%\) interest. She earned \(7.25 \%\) interest on the total investment. How much money did she put in each account?

Sam invested \(\$ 48,000,\) some at \(6 \%\) interest and the rest at \(10 \%\). How much did he invest at each rate if he received \(\$ 4,000\) in interest in one year?

Arnold invested \(\$ 64,000\), some at \(5.5 \%\) interest and the rest at \(9 \% .\) How much did he invest at each rate if he received \(\$ 4,500\) in interest in one year?