Rick and tom rented party halls. the celebrations party hall charged rick a rental fee of $65, including music, and $25 per guest. the feast party hall charged tom a rental fee of $40, $25 for music, and $25 per guest.

if each of them spent the same amount of money, how many guests attended rick and tom's party?

a.
five more guests attended rick's party than tom's party.
b.
fifteen more guests attended tom's party than rick's party.
c.
the same number of guests attended rick and tom's party.
d.
twenty-five more guests attended rick's party than tom's party.

  C. The same number of guests attended Rick and Tom's party.

Step-by-step explanation:

Let R and T represent the number of guests at Rick's and Tom's parties, respectively. The charges Rick and Tom paid are equal, so we have ...

  65 +25R = 40+25+25T

  25R = 25T . . . . . . . . . . . . subtract 65

  R = T . . . . . . . . . . . . . . . . . divide by 25

The number of guests at each party is the same.

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x

it is rigid.; it is isometric. ; the size is preserved.

step-by-step explanation:

a translation is called an isometry; these are transformations that preserve congruence between pre-images and images.

they are also called rigid transformations, as the only thing that can happen to a pre-image is that it is moved or turned, not stretched or shrunk.

since congruence is preserved, the size is preserved.