Chapter 7

Construct a mathematical model given the following. \(y\) is inversely proportional to \(x,\) and \(y=3\) when \(x=9\).

What happens to the P/E ratio when earnings decrease?

Multiply. (Assume all denominators are nonzero.) $$ 100-y 2 y-10 \cdot 25 y 2 y+10 $$

Solve. $$1-3 x-5 x(3 x-4)=-1 x$$

Simplify. $$ 15 x 2-1 x $$

A passenger car averages 16 miles per hour faster than the bus. If the bus travels 56 miles in the same time it takes the passenger car to travel 84 miles, then what is the speed of each?

Simplify. (Assume all denominators are nonzero.) $$ 1 x+15125-1 x 2 $$

Construct a mathematical model given the following. \(y\) is inversely proportional to \(x,\) and \(y=21\) when \(x=3\).

What happens to the P/E ratio when earnings increase?

Solve. $$x 2=14 x+3$$

A light aircraft travels 2 miles per hour less than twice as fast as a passenger car. If the passenger car can travel 231 miles in the same time it takes the aircraft to travel 455 miles, then what is the average speed ofeach?

Construct a mathematical model given the following. \(y\) varies inversely as \(x,\) and \(y=2\) when \(x=1 / 8\).

State the restrictions to the domain. \(13 x\)

Solve. $$3 \times 2=x+13-x$$

Simplify. $$ 1 x-12 y $$

Mary can run 1 mile per hour more than twice as fast as Bill can walk. If Bill can walk 3 miles in the same time it takes Mary to run 7.2 miles, then what is Bill's average walking speed?

Simplify. (Assume all denominators are nonzero.) $$ 14+1 x 1 x 2-116 $$

Construct a mathematical model given the following. \(y\) varies inversely as \(x,\) and \(y=3 / 2\) when \(x=1 / 9\).

Solve. $$6=3 x+3 x-1$$

Simplify. $$ 1 y-2 $$

An airplane traveling with a 20-mile-per-hour tailwind covers 270 miles. On the return trip against the wind, it covers 190 miles in the same amount of time. What is the speed of the airplane in still air?

Simplify. (Assume all denominators are nonzero.) $$ 16-1 x 21 x-4 $$

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and \(z\), where \(y=8\) when \(x=4\) and \(z=1 / 2\).

Simplify. $$ 3 y+2-4 $$

A jet airliner traveling with a 30-mile-per-hour tailwind covers 525 miles in the same amount of time it is able to travel 495 miles after the tailwind eases to 10 miles per hour. What is the speed of the airliner in still air?

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and \(z\), where \(y=24\) when \(x=1 / 3\) and \(z=9\).

Solve. $$2+2 x-3=3(x-1) x-3$$

A boat averages 16 miles per hour in still water. With the current, the boat can travel 95 miles in the same time it travels 65 miles against it. What is the speed of the current?

Simplify. $$ 2 x+4+2 $$

Construct a mathematical model given the following. \(y\) is jointly proportional to \(x\) and \(z\), where \(y=2\) when \(x=1\) and \(z=3\).

State the restrictions to the domain. $$ 15 x-1 $$

Solve. $$x x-1+16 x-1=x(x-1)(6 x-1)$$

A river tour boat averages 7 miles per hour in still water. If the total 24-mile tour downriver and 24 miles back takes 7 hours, then how fast is the river current?

Simplify. (Assume all denominators are nonzero.) $$ 12 x-4314 x 2-169 $$

Construct a mathematical model given the following. \(y\) is jointly proportional to \(x\) and \(z\), where \(y=15\) when \(x=3\) and \(z=7\).

Solve. $$12 \times 2-81=\mid x+9-2 x-9$$

If the river current flows at an average 3 miles per hour, then a tour boat makes the 9 -mile tour downstream with the current and back the 9 miles against the current in 4 hours. What is the average speed of the boat in still water?

Simplify. $$ 3 x+1+1 x $$

Simplify. (Assume all denominators are nonzero.) $$ 225-12 x 215-12 x $$

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and \(z,\) where \(y=2 / 3\) when \(x=1 / 2\) and \(z=12\).

State the restrictions to the domain. $$ x-95 x(x-2) $$

Solve. $$14 \times 2-49=2 x-7-3 x+7$$

Jane rowed her canoe against a 1-mile-per-hour current upstream 12 miles and then returned the 12 miles back downstream. If the total trip took 5 hours, then at what speed can Jane row in still water?

Simplify. $$ 1 x-1-2 x $$

Simplify. (Assume all denominators are nonzero.) $$ 425-14 x 215+14 x $$

Construct a mathematical model given the following. \(y\) varies jointly as \(x\) and \(z\), where \(y=5\) when \(x=3 / 2\) and \(z=2 / 9\).

State the restrictions to the domain. $$ 1(x-3)(x+6) $$

Jose drove 15 miles to pick up his sister and then returned home. On the return trip, he was able to average 15 miles per hour faster than he did on the trip to pick her up. If the total trip took 1 hour, then what was Jose's average speed on the return trip?

Simplify. $$ 1 x-3+1 x+5 $$

Construct a mathematical model given the following. \(y\) varies directly as the square of \(x,\) where \(y=45\) when \(x=3\).