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$36a + 28.3w = 100$ $\newline$ A bottle contains $100$ milliliters of a solution of alcohol and water at room temperature. The equation shows the possible amounts of alcohol, $a$ , and water, $w$ , in ounces. What is the volume of $1$ ounce of alcohol at room temperature in milliliters? $\newline$ Choose $1$ answer: $\newline$ (A) $0.03$ $\newline$ (B) $2.8$ $\newline$ (C) $28.3$ $\newline$ (D) $36$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q.

36a + 28.3w = 100

\newline

A bottle contains

100

milliliters of a solution of alcohol and water at room temperature. The equation shows the possible amounts of alcohol,

a

, and water,

w

, in ounces. What is the volume of

1

ounce of alcohol at room temperature in milliliters?

\newline

Choose

1

answer:

\newline

(A)

0.03

\newline

(B)

2.8

\newline

(C)

28.3

\newline

(D)

36

Identify Equation: Identify the given equation and what it represents. $\newline$ The equation $36a + 28.3w = 100$ represents the total volume of the solution in milliliters, where ' $a$ ' is the volume of alcohol in ounces and ' $w$ ' is the volume of water in ounces.
Conversion Factor: Understand the conversion between ounces and milliliters. $\newline$ $1$ ounce is approximately $29.5735$ milliliters. This conversion factor will be used to find the volume of $1$ ounce of alcohol in milliliters.
Isolate Alcohol Variable: Isolate the alcohol variable $a$ in the equation. $\newline$ To find the volume of $1$ ounce of alcohol, we need to isolate $a$ in the equation. However, since we are looking for the volume of $1$ ounce, we can directly use the conversion factor instead of manipulating the equation.
Convert to Milliliters: Convert $1$ ounce of alcohol to milliliters using the conversion factor. $1$ ounce of alcohol is $1 \times 29.5735$ milliliters.
Calculate Volume: Calculate the volume of $1$ ounce of alcohol in milliliters. $\newline$ Volume of $1$ ounce of alcohol = $29.5735$ milliliters.
Match with Answer Choices: Match the calculated volume with the given answer choices. $\newline$ The calculated volume of $1$ ounce of alcohol in milliliters is $29.5735$ , which is not listed in the answer choices. However, it is closest to answer choice $(C)$ $28.3$ , which seems to be a rounding of the actual conversion factor.

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