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Zorluk: OrtaRatios, Rates, and Proportions

In a hydroponic farming system, a nutrient solution is created by mixing a liquid fertilizer concentrate with water in a ratio of 33 to 5050 by volume. To fill a reservoir, a technician needs to prepare a total of 318318 liters of this nutrient solution. How many liters of the liquid fertilizer concentrate are required to prepare the solution?

Cevap: 18 liters

Cevap

18
To find the amount of liquid fertilizer concentrate needed, we first express the ratio in terms of the total mixture. The ratio of concentrate to water is 33 to 5050, meaning there are 33 parts of concentrate for every 5050 parts of water, making a total of 3+50=533 + 50 = 53 parts. Since the total volume of the solution is 318318 liters, each part represents 31853=6\frac{318}{53} = 6 liters. The amount of concentrate required is 33 parts, which corresponds to 3×6=183 \times 6 = 18 liters.

Adım Adım Çözüm

1
Calculate the total parts represented in the ratio of liquid fertilizer concentrate to water.
The total number of parts is 3+50=533 + 50 = 53.
Since the ratio of concentrate to water is 33 to 5050, the entire nutrient solution is divided into 5353 equal parts.
2
Find the volume of solution that corresponds to one part.
One part is equal to 31853=6\frac{318}{53} = 6 liters.
Dividing the total volume of the nutrient solution (318318 liters) by the total number of parts (5353) gives the volume of a single part.
3
Calculate the total volume of liquid fertilizer concentrate needed.
The volume of concentrate required is 3×6=183 \times 6 = 18 liters.
Since the concentrate accounts for 33 parts of the total mixture, multiplying the volume of one part by 33 gives the total amount of concentrate needed.

Anahtar Kavram

Solving part-to-whole ratio problems by determining the value of a single unit or part from a given total quantity.

Alternatif Yöntem

Let the volume of the fertilizer concentrate be 3x3x and the volume of water be 50x50x. The total volume of the nutrient solution is 3x+50x=53x3x + 50x = 53x. Given that the total volume is 318318 liters, we can set up the equation 53x=31853x = 318. Solving for xx gives x=6x = 6. The volume of the concentrate is 3x=3(6)=183x = 3(6) = 18 liters.
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