A botanical garden conservatory uses a specialized organic fertilizer mixture containing f… — ACT

A botanical garden conservatory uses a specialized organic fertilizer mixture containing $f$ pounds of nutrient concentrate. The concentrate is divided equally into $14$ separate watering reservoirs. If each reservoir receives exactly $2.5$ pounds of concentrate, which of the following equations correctly models this situation?

$\frac{f}{14} = 2.5$ Answer
B
$14f = 2.5$
C
$f - 14 = 2.5$
D
$\frac{14}{f} = 2.5$
E
$f + 2.5 = 14$

Answer

The equation

\frac{f}{14} = 2.5

correctly models the situation.

Dividing the total amount of nutrient concentrate (

f

) equally into

14

reservoirs means dividing

f

14

. Setting this equal to the amount per reservoir (

2.5

pounds) yields

\frac{f}{14} = 2.5

Step-by-Step Solution

Identify the total quantity and how it is shared or split.

The total amount of nutrient concentrate is

f

pounds, divided equally into

14

reservoirs.

Equal sharing or division of a total quantity

f

into

14

equal parts is expressed algebraically as

\frac{f}{14}

Equate the expression for one part to the given value per reservoir.

\frac{f}{14} = 2.5

Each reservoir gets

2.5

pounds, so the portion in one reservoir,

\frac{f}{14}

, must equal

2.5

Key Concept

Translating verbal descriptions of equal division into one-step algebraic equations

Question

Answer

Step-by-Step Solution

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