What is the Unitary Method?

The Unitary Method is a technique used to solve problems by finding the value of a single unit first and then multiplying it to find the value of multiple units. For example, if 5 apples cost $10, the cost of 1 apple is $10/5 = $2.

If 6 workers can complete a task in 12 days, how long will it take 4 workers to complete the same task?

Hint: First, find the work done by one worker in one day.

First, calculate the total work in worker-days: 6 workers * 12 days = 72 worker-days. If 4 workers are working, the number of days required is 72 worker-days / 4 workers = 18 days.

A car travels 240 kilometers using 20 liters of fuel. How much fuel will be required for 150 kilometers?

Hint: Determine the fuel consumption per kilometer first.

First, find the fuel consumption per kilometer: 20 liters / 240 kilometers = 0.0833 liters per kilometer. Then, for 150 kilometers, the fuel required is 150 kilometers * 0.0833 liters/kilometer ≈ 12.5 liters.

A recipe requires 3 cups of flour for 4 servings. How much flour is needed for 10 servings?

Hint: Find the amount of flour needed per serving first.

First, find the flour per serving: 3 cups / 4 servings = 0.75 cups per serving. For 10 servings, the flour needed is 10 servings * 0.75 cups/serving = 7.5 cups.

A man can read 30 pages in 2 hours. How many pages can he read in 5 hours?

Hint: Find the reading rate per hour first.

First, find the reading rate: 30 pages / 2 hours = 15 pages per hour. In 5 hours, he can read 5 hours * 15 pages/hour = 75 pages.

If 8 kg of rice costs $32, how much would 5 kg cost?

Hint: Determine the cost per kg first.

First, find the cost per kg: $32 / 8 kg = $4 per kg. Therefore, 5 kg would cost 5 kg * $4/kg = $20.

If 12 pens cost $24, what would be the cost of 20 pens?

Hint: Find the cost of one pen first.

First, find the cost of one pen: $24 / 12 pens = $2 per pen. Therefore, the cost for 20 pens would be 20 pens * $2/pen = $40.

If 4 workers complete a task in 10 days, how long will 8 workers take to complete the same task?

Hint: Find total worker-days to solve.

Total work = 4 workers * 10 days = 40 worker-days. If 8 workers are working, days required = 40 worker-days / 8 workers = 5 days.

A recipe requires 2 kg of sugar for 5 cakes. How much sugar is needed for 8 cakes?

Hint: Calculate sugar per cake first.

First, find the sugar per cake: 2 kg / 5 cakes = 0.4 kg per cake. For 8 cakes, sugar needed = 8 cakes * 0.4 kg/cake = 3.2 kg.

If 10 meters of fabric costs $50, how much would 25 meters cost?

Hint: Find the cost per meter first.

First, find the cost per meter: $50 / 10 meters = $5 per meter. Therefore, the cost for 25 meters would be 25 meters * $5/meter = $125.