Dezeree received $100 gift card and needs new sweaters for school the sweaters cost $27.50 each write an equation of determine how many sweaters she can buy and spend exactly a 100

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.