To determine how many sweaters Dezeree can buy with her $100 gift card, we can write the equation:

\[
27.50x = 100
\]

where \( x \) is the number of sweaters she can buy.

Now, we will solve for \( x \):

1. Divide both sides of the equation by $27.50:

\[
x = \frac{100}{27.50}
\]

2. Calculate the right side:

\[
x = \frac{100}{27.50} = 3.63636\ldots
\]

Since she cannot buy a fraction of a sweater, we need to determine how many whole sweaters she can afford. Therefore, we take the whole number part:

\[
x = 3
\]

Now, we can verify if buying 3 sweaters is a viable solution by calculating the total cost:

\[
\text{Total cost} = 27.50 \times 3 = 82.50
\]

Since $82.50 is less than $100, she can buy 3 sweaters and still have some money left over.

Now, 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 $100, Dezeree cannot buy 4 sweaters.

In conclusion, the viable solution is:

Dezeree can buy **3 sweaters** and spend **$82.50**, leaving her with **$17.50** left on her gift card.
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