A nursery technician prepares a liquid fertilizer mixture using nitrogen, phosphorus, and … — ACT

A nursery technician prepares a liquid fertilizer mixture using nitrogen, phosphorus, and potassium in a volume ratio of $4 : 2 : 1$ , respectively. A storage tank currently holds $35\text{ liters}$ of this mixture. If the technician adds $6\text{ liters}$ of pure nitrogen to the tank, what is the ratio of nitrogen to phosphorus in the resulting mixture?

A
$5 : 1$
$13 : 5$ Cevap
C
$13 : 10$
D
$5 : 4$
E
$26 : 41$

Cevap

The ratio of nitrogen to phosphorus in the resulting mixture is

13 : 5

The original

35\text{ liters}

contains

7

equal parts of

5\text{ liters}

each. Nitrogen represents

4

parts (

20\text{ liters}

) and phosphorus represents

2

parts (

10\text{ liters}

). Adding

6\text{ liters}

of nitrogen brings the nitrogen amount to

26\text{ liters}

. Comparing

26\text{ liters}

of nitrogen to

10\text{ liters}

of phosphorus yields the ratio

26 : 10

, which simplifies to

13 : 5

Adım Adım Çözüm

Find the total number of parts in the original ratio.

4 + 2 + 1 = 7\text{ total parts}

To determine the volume of each component, calculate the total proportion of the mixture.

Calculate the initial volume of nitrogen and phosphorus in

35\text{ liters}

of solution.

\text{Nitrogen} = \frac{4}{7} \times 35 = 20\text{ liters}; \quad \text{Phosphorus} = \frac{2}{7} \times 35 = 10\text{ liters}.

Multiply each component's fraction by the total volume of

35\text{ liters}

Add

6\text{ liters}

to the initial volume of nitrogen.

\text{New Nitrogen volume} = 20 + 6 = 26\text{ liters}.

Only nitrogen is added to the tank, while phosphorus remains unchanged at

10\text{ liters}

Write and simplify the new ratio of nitrogen to phosphorus.

\frac{26}{10} = \frac{13}{5} \implies 13 : 5.

Divide both terms by their greatest common factor,

2

Anahtar Kavram

Partitioning a total quantity into parts using extended ratios and adjusting part quantities.

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Adım Adım Çözüm

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