An environmental research vessel collects deep-sea water samples. A marine biologist deter… — ACT

An environmental research vessel collects deep-sea water samples. A marine biologist determines that $\frac{4}{7}$ of the total capacity $V$ (in liters) of a specialized storage tank is occupied by seawater collected during a single dive. If the seawater collected during this dive measures exactly $28$ liters, which of the following equations correctly models this relationship, and what is the total capacity $V$ of the storage tank in liters?

$\frac{4}{7}V = 28$ ; $V = 49$ Answer
B
$\frac{4}{7}V = 28$ ; $V = 16$
C
$V - \frac{4}{7} = 28$ ; $V = 28.57$
D
$\frac{7}{4}V = 28$ ; $V = 16$
E
$\frac{4}{7} + V = 28$ ; $V = 27.43$

Answer

The correct equation is

\frac{4}{7}V = 28

, which yields a total tank capacity of

V = 49

liters.

The phrase '

\frac{4}{7}

of the total capacity

V

' signifies the product of the fraction and the variable

V

. Setting this product equal to the given volume of

28

liters yields the equation

\frac{4}{7}V = 28

. Isolating

V

requires dividing both sides by

\frac{4}{7}

, which is equivalent to multiplying

28

by the reciprocal

\frac{7}{4}

. Simplifying

28 \cdot \frac{7}{4}

gives

(28 \div 4) \cdot 7 = 7 \cdot 7 = 49

liters.

Step-by-Step Solution

Translate the verbal description into an algebraic equation.

\frac{4}{7}V = 28

The phrase '

\frac{4}{7}

of the total capacity

V

' means multiplying

\frac{4}{7}

V

, and this portion is equal to

28

liters.

Solve the one-step equation for

V

by multiplying both sides by the reciprocal of

\frac{4}{7}

V = 28 \times \frac{7}{4}

Multiplying by the reciprocal

\frac{7}{4}

isolates

V

on the left side of the equation.

Simplify the arithmetic calculation.

V = 7 \times 7 = 49

Dividing

28

4

gives

7

, and multiplying

7

7

results in

49

liters.

Key Concept

Formulating and solving one-step multiplication equations involving fractional coefficients.

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