Dezeree received a $100 gift card and needs new sweaters for school. The sweaters cost $27.50 each. Write an equation to determine how many sweaters she can buy and spend exactly $100, solve it, and determine if the value is a viable solution

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 she can buy. The cost of each sweater is $27.50. Therefore, the total cost for \( x \) sweaters can be represented by the equation:

\[
27.50x = 100
\]

To solve for \( x \), divide both sides of the equation by 27.50:

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

Calculating the right side:

\[
x = \frac{100}{27.50} = 3.63636363636...
\]

Since Dezeree cannot buy a fractional part of a sweater, we need to round down to the nearest whole number. Therefore, she can buy 3 sweaters.

To verify if this is a viable solution, we can calculate the total cost if she buys 3 sweaters:

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

Now, let's check how much money she would have left:

\[
\text{Remaining balance} = 100 - 82.50 = 17.50
\]

If she tries to buy 4 sweaters:

\[
\text{Total cost} = 27.50 \times 4 = 110.00
\]

This cost exceeds her gift card limit of $100, confirming that 3 sweaters is indeed the maximum she can buy without exceeding the $100 limit. Thus, the number of sweaters Dezeree can buy is **3**, which is a viable solution.