함수 전체 문제

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.

• ⓐ Write the equation that relates P and n.
• ⓑ How much money would she earn if she sold 4 necklaces?

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.

• ⓐ Write the equation that relates P and g.
• ⓑ How much would 33 gallons cost Eric?

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.

• ⓐ Write the equation that relates a and p.
• ⓑ How many apples would Terri need for six 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.

• ⓐ Write the equation that relates d and v.
• ⓑ How far would he travel before stopping for lunch at a rate of 65 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.

• ⓐ Write the equation that relates the price to the number of gallons.
• ⓑ 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.

• ⓐ Write the equation that relates the distance to the number of hours.
• ⓑ 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.

• ⓐ Write the equation that relates the mass to the volume.
• ⓑ 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.

• ⓐ Write the equation that relates the length of the spring to the weight.
• ⓑ 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.

• ⓐ Write the equation that relates the distance to the time.
• ⓑ 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.

• ⓐ Write the equation that relates the load to the diagonal of the cross-section.
• ⓑ 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.

• ⓐ Write the equation that relates the area to the radius.
• ⓑ 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,

• ⓐ Write the equation that relates the distance to the time.
• ⓑ 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 $y.$