8.9 Use direct and inverse variation  (Page 5/10)

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

1. ⓐ Write the equation that relates the price to the number of gallons.
2. ⓑ How much will it cost Jesse for 15 gallons of gas?

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

1. ⓐ Write the equation that relates the distance to the number of hours.
2. ⓑ How far can Sally travel in 6 hours?

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

1. ⓐ Write the equation that relates the mass to the volume.
2. ⓑ What is the volume of this liquid if its mass is 128 kilograms?

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.

1. ⓐ Write the equation that relates the length of the spring to the weight.
2. ⓑ What weight of watermelon would stretch the spring 6 inches?

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

1. ⓐ Write the equation that relates the distance to the time.
2. ⓑ How far will the ball fall in 7 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.

1. ⓐ Write the equation that relates the load to the diagonal of the cross-section.
2. ⓑ What load will a beam with a 10 inch diagonal support?

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.

1. ⓐ Write the equation that relates the area to the radius.
2. ⓑ What is the area of a personal pizza with a radius 4 inches?

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

1. ⓐ Write the equation that relates the distance to the time.
2. ⓑ How far will the ball have fallen in 8 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.

1. ⓐ Write the equation that relates the mpg to the car’s weight.
2. ⓑ What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?

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

1. ⓐ Write the equation that relates the car’s value to its age.
2. ⓑ What will be the value of Jackie’s car when it is 15 years old ?