A fuel tank initially contains 60 gallons of a fuel mixture that is 10\% ethanol and 90\% … — GMAT

A fuel tank initially contains $60$ gallons of a fuel mixture that is $10\%$ ethanol and $90\%$ gasoline by volume. A mechanic removes $x$ gallons of this mixture and replaces it with an equal volume of pure ethanol to obtain a new mixture that is $25\%$ ethanol by volume. What is the value of $x$ ?

Cevap: 10 gallons

Cevap

The volume of fuel mixture that must be removed and replaced with pure ethanol is

10

gallons.

Replacing

10

gallons of the

10\%

ethanol fuel with pure ethanol removes

1

gallon of ethanol and adds

10

gallons of pure ethanol. The total ethanol in the tank becomes

6 - 1 + 10 = 15

gallons, which represents exactly

25\%

of the total

60

-gallon volume.

Adım Adım Çözüm

Calculate the initial volume of ethanol in the tank

Ethanol volume =

0.10 \times 60 = 6

gallons.

Establishes the starting quantity of the solute.

Express the amount of ethanol after removal and replacement in terms of

x

Final ethanol volume =

6 - 0.10x + x = 6 + 0.90x

gallons.

Removing

x

gallons of fuel removes

10\%

ethanol, while adding

x

gallons of pure ethanol adds

100\%

ethanol.

Set up an equation using the target ethanol concentration

6 + 0.90x = 0.25 \times 60 = 15

The final

60

-gallon mixture must contain

25\%

ethanol by volume.

Solve the equation for

x

0.90x = 9 \implies x = 10

Isolates

x

to find the required replacement volume.

Anahtar Kavram

Dilution and fluid replacement in mixture problems

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