To determine how many sweaters Dezeree can buy with her $100 gift card, we can set up the equation based on the cost of the sweaters.
Let \( x \) represent the number of sweaters she can buy. The cost for \( x \) sweaters is given by the equation:
\[ 27.50x = 100 \]
Now, to solve for \( x \), we can divide both sides of the equation by 27.50:
\[ x = \frac{100}{27.50} \]
Calculating the right-hand side:
\[ x = \frac{100}{27.50} \approx 3.63636 \]
Since Dezeree can only buy a whole number of sweaters, we round down to the nearest whole number because buying a fraction of a sweater isn't possible; thus, she can buy at most 3 sweaters.
Next, let's check how much money she will spend if she buys 3 sweaters:
\[ \text{Total cost for 3 sweaters} = 27.50 \times 3 = 82.50 \]
Now let's see how much money would be left over:
\[ \text{Remaining balance} = 100 - 82.50 = 17.50 \]
Also, let's check if she can buy 4 sweaters:
\[ \text{Total cost for 4 sweaters} = 27.50 \times 4 = 110.00 \]
Since $110.00 exceeds her $100 gift card limit, she cannot buy 4 sweaters.
Thus, the number of sweaters that Dezeree can buy and spend exactly $100 is 3.
In conclusion, the viable solution is:
\[ \boxed{3} \]
If fraud was considered, her remaining balance would be $17.50 after purchasing 3 sweaters.