Joint Variation Word Problems: Equations & Graphs - Grade 8

A car's fuel consumption varies jointly with the distance traveled and the weight of the car. If a car weighing 1,500 kg consumes 10 liters of fuel to travel 100 km, how much fuel will it consume to travel 250 km with a weight of 2,000 kg?

• 25 liters

• 33.34 liters

• 40 liters

• 50 liters

The area of a rectangle varies jointly with its length and width. If a rectangle with a length of 5 meters and a width of 3 meters has an area of 15 square meters, what will be the area of a rectangle with a length of 8 meters and a width of 4 meters?

• 40 square meters

• 32 square meters

• 20 square meters

• 24 square meters

The cost of producing a certain product varies jointly with the number of units produced and the cost per unit. If producing 100 units at $5 each costs $500, how much will it cost to produce 200 units at $6 each?

• $1200

• $1500

• $1000

• $800

The brightness of a light bulb varies jointly with the voltage and the current. If a bulb operates at 120 volts and 2 amps, producing a brightness of 240 lumens, what will be the brightness if the voltage is increased to 240 volts while keeping the current the same?

• 480 lumens

• 360 lumens

• 240 lumens

• 600 lumens

The volume of a gas varies jointly with its temperature and the pressure applied. If a gas has a volume of 10 liters at 300 K and 2 atm, what will be the volume at 600 K and 4 atm?

• 10 liters

• 15 liters

• 20 liters

• 5 liters

A recipe for a cake requires flour, sugar, and eggs in a joint variation relationship. If a cake that serves 8 people uses 2 cups of flour, 1 cup of sugar, and 3 eggs, how much of each ingredient is needed for a cake that serves 20 people?

• 4 cups of flour, 2 cups of sugar, 6 eggs

• 6 cups of flour, 3 cups of sugar, 8 eggs

• 5 cups of flour, 2.5 cups of sugar, 7.5 eggs

• 3 cups of flour, 1 cup of sugar, 5 eggs

The speed of a boat varies jointly with the current and the power of the engine. If a boat with a 100 HP engine moves at 30 km/h in a current of 5 km/h, what will be its speed in a current of 10 km/h with the same engine power?

• 45 km/h

• 50 km/h

• 60 km/h

• 25 km/h

The strength of a material varies jointly with its thickness and the type of material. If a steel beam that is 10 cm thick can support 500 kg, how much weight can a 15 cm thick steel beam support?

• 750 kg

• 300 kg

• 600 kg

• 900 kg

The profit from selling a product varies jointly with the number of items sold and the price per item. If selling 50 items at $20 each yields a profit of $500, what will be the profit from selling 100 items at $25 each?

• 1250

• $750

• $1500

• $1000

The amount of paint needed varies jointly with the area to be painted and the number of coats. If 1 gallon of paint covers 400 square feet with 2 coats, how much paint is needed for a 1,000 square foot area with 3 coats?

• 4.5 gallons

• 5 gallons

• 3.75 gallons

• 2.5 gallons