Exam 7: Systems of Equations

Solve the problem. -The perimeter of a triangle is $45 \mathrm{~cm}$ . The triangle is isosceles now, but if its base were lengthened by $3 \mathrm{~cm}$ and each leg were shortened by $3 \mathrm{~cm}$ , it would be equilateral. Find the base of the original triangle.

Solve the problem. -A plane flies 420 miles with the wind and 320 miles against the wind in the same length of time. If the speed of the wind is $30 \mathrm{mph}$ , what is the speed of the plane in still air?

Solve the problem. -The perimeter of a rectangle is $58 \mathrm{~cm}$ . One side is $11 \mathrm{~cm}$ longer than the other side. Find the lengths of the sides.

Solve the problem. -Ellen wishes to mix candy worth $\$ 1.11$ per pound with candy worth $\$ 3.86$ per pound to form 16 pounds of a mixture worth $\$ 2.31$ per pound. How many pounds of the more expensive candy should she use?

Solve the problem. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 99$ for 3 days and 300 miles, while Mary was charged $\$ 178$ for 5 days and 600 miles. What does Best Rental charge per day and per mile?

Solve by the substitution method. - x-4y =-27 4x-5y =-53

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 6 miles per hour, and Delvis is traveling at the speed of 12 miles per hour. In 4 hours what is the distance between them?

Solve the system by graphing. - $3 x+2 y=5$ $-6 x-4 y=5$

Solve using the substitution method. - $y=2 x+4$ $3 x+y=34$

Solve by the substitution method. - $8 x-7 y=100$ $3 x-4 y=43$

Solve the system by graphing. - $3 x+y=16$ $12 x+4 y=64$

Solve the problem. -The sum of two numbers is 45 and their difference is 9 . Find the numbers.

Solve the problem. -The speed of a stream is $4 \mathrm{mph}$ . If a boat travels 40 miles downstream in the same time that it takes to travel 20 miles upstream, what is the speed of the boat in still water?

Solve the problem. -Two angles are supplementary, and one is $40^{\circ}$ more than three times the other. Find the smaller angle.

Solve the problem. -How many liters of a $30 \%$ alcohol solution must be mixed with 60 liters of a $70 \%$ solution to get a $40 \%$ solution?

Solve the problem. -Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 21 pounds of feed worth $\$ 0.17$ per pound by mixing one kind worth $\$ 0.11$ per pound with another worth $\$ 0.22$ per pound. How many pounds of the cheaper kind should they use in the mix? Round to the nearest whole pound if necessary.

Solve by elimination. - $x-6 y=-59$ $6 \mathrm{x}-7 \mathrm{y}=-93$

Solve the system by graphing. - $5 x+y=27$ $5 x+y=42$

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 6 miles per hour. In how many hours will they be 60 miles apart?

Solve using the elimination method. - $-7 x-4 y=-58$ $5 \mathrm{x}+4 \mathrm{y}=46$