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Tammy rents an apartment close to her school campus. The amount that she spends on rent is given by the equation [tex]r = 355m[/tex], where [tex]r[/tex] is the amount spent on rent and [tex]m[/tex] is the number of months she stays in the apartment. What is the constant of proportionality ([tex]r[/tex] to [tex]m[/tex]) for this proportional relationship?

A. [tex]\frac{1}{355}[/tex]
B. [tex]\frac{1}{1775}[/tex]
C. 177.5
D. 355

Sagot :

GinnyAnswer
To determine the constant of proportionality for the proportional relationship given by the equation [tex]\( r = 355m \)[/tex], let's examine the equation step-by-step.

The given equation relates [tex]\( r \)[/tex] (the amount of rent) to [tex]\( m \)[/tex] (the number of months) by the following formula:
[tex]\[ r = 355m \][/tex]

In this type of linear proportional relationship, the constant of proportionality is the coefficient of [tex]\( m \)[/tex]. This coefficient is the constant value that [tex]\( r \)[/tex] is multiplied by to yield the amount of rent for any given number of months [tex]\( m \)[/tex].

From the equation, we can see that:
[tex]\[ r = 355 \times m \][/tex]

Comparing this with the general form of a proportional relationship [tex]\( r = k \times m \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality, it is clear that [tex]\( k = 355 \)[/tex].

Thus, the constant of proportionality [tex]\( k \)[/tex], which relates [tex]\( r \)[/tex] to [tex]\( m \)[/tex] in the given equation, is [tex]\( 355 \)[/tex].

Therefore, the correct answer is:
D. 355
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