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P=(19)/(2)+(4)/(25)d
The amount of paint,
P, in pints, that an art studio can buy with
d dollars is given by the equation. What is the best interpretation of
(4)/(25) as shown in the equation?
Choose 1 answer:
(A) The paint costs
(4)/(25) of a dollar per pint.
(B) One dollar can buy
(4)/(25) of a pint of paint.
(C) The art studio started with
(4)/(25) of a pint of paint.
(D) The art studio can purchase at most
(4)/(25) of a pint of paint.

$P=\frac{19}{2}+\frac{4}{25} d$ $\newline$ The amount of paint, $P$ , in pints, that an art studio can buy with $d$ dollars is given by the equation. What is the best interpretation of $\frac{4}{25}$ as shown in the equation? $\newline$ Choose $1$ answer: $\newline$ (A) The paint costs $\frac{4}{25}$ of a dollar per pint. $\newline$ (B) One dollar can buy $\frac{4}{25}$ of a pint of paint. $\newline$ (C) The art studio started with $\frac{4}{25}$ of a pint of paint. $\newline$ (D) The art studio can purchase at most $\frac{4}{25}$ of a pint of paint.

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Write linear functions: word problems

Full solution

Q.

P=\frac{19}{2}+\frac{4}{25} d

\newline

The amount of paint,

P

, in pints, that an art studio can buy with

d

dollars is given by the equation. What is the best interpretation of

\frac{4}{25}

as shown in the equation?

\newline

Choose

1

answer:

\newline

(A) The paint costs

\frac{4}{25}

of a dollar per pint.

\newline

(B) One dollar can buy

\frac{4}{25}

of a pint of paint.

\newline

(C) The art studio started with

\frac{4}{25}

of a pint of paint.

\newline

(D) The art studio can purchase at most

\frac{4}{25}

of a pint of paint.

Understand the equation: Understand the equation. $\newline$ The equation $P=\frac{19}{2}+\frac{4}{25}d$ represents the amount of paint $P$ in pints that can be bought with $d$ dollars. The term $\frac{19}{2}$ is a constant, which suggests a starting amount of paint that can be bought without spending any money. The term $\frac{4}{25}d$ represents the variable part of the equation, which changes depending on the amount of money $d$ spent.
Analyze the term: Analyze the term $(4)/(25)d$ . $\newline$ The term $(4)/(25)d$ suggests that for every dollar $d$ spent, $(4)/(25)$ pints of paint can be bought. This is because $d$ represents the number of dollars, and multiplying it by $(4)/(25)$ gives the additional pints of paint that can be bought with those dollars.
Interpret the coefficient: Interpret the coefficient $(\frac{4}{25})$ . The coefficient $(\frac{4}{25})$ in front of the variable $d$ tells us how much paint in pints can be bought per dollar. Therefore, for every dollar spent, $(\frac{4}{25})$ pints of paint can be purchased.
Match the interpretation: Match the interpretation to the given options. $\newline$ Based on the analysis, the coefficient $(4)/(25)$ means that one dollar can buy $(4)/(25)$ of a pint of paint. This matches option (B) from the given choices.

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