KAILANGAN KO LANG NG 3/5 NA MASOLVE WITH SOLUTION. SA PAPEL PO GAWIN PARA MAS MAINTINDIHAN KO PO, THANK YOU.Solve the followig problems using the concepts learned in direct variation.1. A recipe for cake requires 3 teaspoonfuls of yeast for 5 cupfuls of flour. How much yeast would be needed for 18 cupfuls of flour?2. Liza, a professional typist, can type 70 words per minute. How many minutes will it take her to finish a manuscript of 1610 words?3. At a local market, a kilo of pork costs 240 pesos. If you plan to buy 2 kilos, how much will you have to pay?4. The weight on the moon varies directly with the weight on Earth. A person that weighs 70 kg on Earth weighs 12 kg on the moon. How much will a person who weigh 120 kg on Earth weighs on the moon?5. The distance that a body falls from rest varies directly as the square of the time it falls. If a ball falls 180 feet in two seconds, how far will the ball fall in five seconds?
Answer (1)
Answer:Here are the solutions to the problems using the concepts of direct variation: 1. Yeast and FlourUnderstanding Direct Variation: The amount of yeast needed varies directly with the amount of flour. This means if you increase the flour, you also need to increase the yeast proportionally.Setting up the Proportion: Let 'y' be the amount of yeast needed for 18 cupfuls of flour. We can set up a proportion: 3 teaspoons / 5 cupfuls = y teaspoons / 18 cupfulsSolving for y: Cross-multiply and solve for y: 3 * 18 = 5 * y 54 = 5y y = 10.8 teaspoonsAnswer: You would need 10.8 teaspoons of yeast for 18 cupfuls of flour. 2. Typing TimeUnderstanding Direct Variation: The number of words typed varies directly with the time taken. More time means more words typed.Setting up the Proportion: Let 't' be the time in minutes to type 1610 words. We can set up a proportion: 70 words / 1 minute = 1610 words / t minutesSolving for t: Cross-multiply and solve for t: 70 * t = 1610 * 1 70t = 1610 t = 23 minutesAnswer: It will take Liza 23 minutes to finish a manuscript of 1610 words. 3. Pork CostUnderstanding Direct Variation: The cost of pork varies directly with the weight. More weight means a higher cost.Setting up the Proportion: Let 'c' be the cost of 2 kilos of pork. We can set up a proportion: 240 pesos / 1 kilo = c pesos / 2 kilosSolving for c: Cross-multiply and solve for c: 240 * 2 = 1 * c 480 = cAnswer: You will have to pay 480 pesos for 2 kilos of pork. 4. Weight on the MoonUnderstanding Direct Variation: The weight on the moon varies directly with the weight on Earth. This means if you increase the weight on Earth, you also increase the weight on the moon proportionally.Setting up the Proportion: Let 'm' be the weight on the moon of a person who weighs 120 kg on Earth. We can set up a proportion: 12 kg / 70 kg = m kg / 120 kgSolving for m: Cross-multiply and solve for m: 12 * 120 = 70 * m 1440 = 70m m = 20.57 kg (approximately)Answer: A person who weighs 120 kg on Earth will weigh approximately 20.57 kg on the moon. 5. Falling DistanceUnderstanding Direct Variation: The distance a body falls varies directly as the square of the time it falls. This means if you increase the time, the distance increases proportionally to the square of the time.Setting up the Proportion: Let 'd' be the distance the ball falls in 5 seconds. We can set up a proportion: 180 feet / (2 seconds)^2 = d feet / (5 seconds)^2 180 feet / 4 = d feet / 25Solving for d: Cross-multiply and solve for d: 180 * 25 = 4 * d 4500 = 4d d = 1125 feetAnswer: The ball will fall 1125 feet in 5 seconds.
