第8章有理式と有理方程式

If $y$ varies directly as $x$ and $y=14,\text{when}x=3$, find the equation that relates $x\text{and}y$.

If $p$ varies directly as $q$ and $p=5,\text{when}q=2$, find the equation that relates $p\text{and}q$.

If $v$ varies directly as $w$ and $v=24,\text{when}w=8$, find the equation that relates $v\text{and}w.$

If $a$ varies directly as $b$ and $a=16,\text{when}b=4$, find the equation that relates $a\text{and}b.$

If $p$ varies directly as $q$ and $p=9.6,\text{when}q=3$, find the equation that relates $p\text{and}q.$

If $y$ varies directly as $x$ and $y=12.4,\text{when}x=4,$ find the equation that relates $x\text{and}y$

If $a$ varies directly as $b$ and $a=6,\text{when}b=\frac{1}{3}$, find the equation that relates $a\text{and}b.$

If $v$ varies directly as $w$ and $v=8,\text{when}w=\frac{1}{2}$, find the equation that relates $v\text{and}w.$

The amount of money Sally earns, P, varies directly with the number, n, of necklaces she sells. When Sally sells 15 necklaces she earns $150.

The price, P, that Eric pays for gas varies directly with the number of gallons, g, he buys. It costs him $50 to buy 20 gallons of gas.

Terri needs to make some pies for a fundraiser. The number of apples, a, varies directly with number of pies, p. It takes nine apples to make two pies.

Joseph is traveling on a road trip. The distance, d, he travels before stopping for lunch varies directly with the speed, v, he travels. He can travel 120 miles at a speed of 60 mph.

The price of gas that Jesse purchased varies directly to how many gallons he purchased. He purchased 10 gallons of gas for $39.80.

The distance that Sarah travels varies directly to how long she drives. She travels 440 miles in 8 hours.

The mass of a liquid varies directly with its volume. A liquid with mass 16 kilograms has a volume of 2 liters.

The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10 pound watermelon on a hanging scale, the spring stretched 5 inches.

The distance an object falls varies directly to the square of the time it falls. A ball falls 45 feet in 3 seconds.

The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. A beam with diagonal 6 inch will support a maximum load of 108 pounds.

The area of a circle varies directly as the square of the radius. A circular pizza with a radius of 6 inches has an area of 113.04 square inches.

The distance an object falls varies directly to the square of the time it falls. A ball falls 72 feet in 3 seconds,

If $y$ varies inversely with $x$ and $y=5$ when $x=4$ find the equation that relates $x$ and $y.$

If $p$ varies inversely with $q$ and $p=2$ when $q=1$ find the equation that relates $p$ and $q.$

If $v$ varies inversely with $w$ and $v=6$ when $w=\frac{1}{2}$ find the equation that relates $v$ and $w.$

If $a$ varies inversely with $b$ and $a=12$ when $b=\frac{1}{3}$ find the equation that relates $a$ and $b.$

The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds and gets 33 mpg on the highway.

A car’s value varies inversely with its age. Jackie bought a 10 year old car for $2,400.

The time required to empty a tank varies inversely as the rate of pumping. It took Janet 5 hours to pump her flooded basement using a pump that was rated at 200 gpm (gallons per minute),

The volume of a gas in a container varies inversely as pressure on the gas. A container of helium has a volume of 370 cubic inches under a pressure of 15 psi.

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. An 11-inch string on a violin has a frequency of 400 cycles per second.

Paul, a dentist, determined that the number of cavities that develops in his patient’s mouth each year varies inversely to the number of minutes spent brushing each night. His patient, Lori, had 4 cavities when brushing her teeth 30 seconds (0.5 minutes) each night.

The number of tickets for a sports fundraiser varies inversely to the price of each ticket. Brianna can buy 25 tickets at $5each.

Boyle’s Law states that if the temperature of a gas stays constant, then the pressure varies inversely to the volume of the gas. Braydon, a scuba diver, has a tank that holds 6 liters of air under a pressure of 220 psi.