Tank P contains 80 liters of a liquid fertilizer solution that is 30\% nitrogen by volume.… — GMAT

Tank P contains $80$ liters of a liquid fertilizer solution that is $30\%$ nitrogen by volume. Tank Q contains $120$ liters of a liquid fertilizer solution that is $15\%$ nitrogen by volume. If $x$ liters of solution are transferred from Tank P into Tank Q, causing the nitrogen concentration in Tank Q to become $20\%$ , what is the value of $x$ ?

A
$20$
B
$30$
C
$40$
$60$ Cevap
E
$80$

Cevap

The volume transferred,

x

, is

60

liters.

The initial amount of nitrogen in Tank Q is

0.15 \times 120 = 18

liters. Transferring

x

liters from Tank P adds

0.30x

liters of nitrogen and increases Tank Q's total volume to

120 + x

liters. Setting the new concentration to

20\%

, we get

\frac{18 + 0.30x}{120 + x} = 0.20

. Solving for

x

gives

18 + 0.30x = 24 + 0.20x \implies 0.10x = 6 \implies x = 60

. Thus,

60

liters must be transferred.

Adım Adım Çözüm

Calculate the initial volume of pure nitrogen in Tank Q.

Initial nitrogen in Tank Q =

15\% \text{ of } 120 = 0.15 \times 120 = 18

liters.

To determine the new concentration, we must know the starting amount of solute.

Express the added nitrogen and the new total volume of Tank Q in terms of

x

Nitrogen added from Tank P =

0.30x

liters; New total volume of Tank Q =

120 + x

liters.

The solution transferred carries

30\%

nitrogen per liter and increases both the nitrogen content and total volume of Tank Q.

Set up the concentration equation for Tank Q and solve for

x

\frac{18 + 0.30x}{120 + x} = 0.20 \implies 18 + 0.30x = 0.20(120 + x) \implies 18 + 0.30x = 24 + 0.20x \implies 0.10x = 6 \implies x = 60.

The concentration is defined as total solute divided by total solution volume.

Anahtar Kavram

Weighted Average and Mixture Equations

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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