To determine how many collectible dolls Mariah can buy, we can set up the equation based on the cost of the dolls and her total budget.
Let \( x \) be the number of dolls Mariah can buy. The cost of each doll is $4.50, and she has $75.00 to spend. The relationship can be expressed with the following equation:
\[ 4.50x \leq 75.00 \]
To find out how many dolls she can purchase, we can solve for \( x \):
\[ x \leq \frac{75.00}{4.50} \]
Calculating the right side:
\[ \frac{75.00}{4.50} = 16.67 \]
Since \( x \) must be a whole number (she can't buy a fraction of a doll), we round down to the nearest whole number:
\[ x \leq 16 \]
Thus, Mariah can buy a maximum of 16 dolls. The equation that represents the situation is:
\[ 4.50x \leq 75.00 \]