To determine how many sweaters Dezeree can buy with her $100 gift card, we can set up the following equation:
Let \( x \) be the number of sweaters Dezeree can buy. The cost of each sweater is $27.50, so the total cost for \( x \) sweaters will be \( 27.50x \).
We want the total cost to equal the amount on her gift card:
\[
27.50x = 100
\]
Now, we will solve for \( x \):
1. Divide both sides of the equation by \( 27.50 \):
\[
x = \frac{100}{27.50}
\]
2. Calculate the value:
\[
x = 3.6363 \ldots
\]
Since Dezeree cannot buy a fraction of a sweater, we round down to the nearest whole number. Thus, she can buy **3 sweaters**.
Now, let's check if buying 3 sweaters will exactly use the $100 gift card:
- Cost of 3 sweaters:
\[
3 \times 27.50 = 82.50
\]
After buying 3 sweaters, she will have some money left over:
\[
100 - 82.50 = 17.50
\]
Let's check if she can afford 4 sweaters:
- Cost of 4 sweaters:
\[
4 \times 27.50 = 110
\]
Since $110 is more than $100, she cannot afford 4 sweaters.
Thus, the viable solution is that Dezeree can buy **3 sweaters** and will have **$17.50 remaining** on her gift card.