To determine how many sweaters Dezeree can buy with a $100 gift card where each sweater costs $27.50, we can set up the following equation:
Let \( x \) be the number of sweaters Dezeree can buy. The cost of \( x \) sweaters is given by:
\[
27.50x = 100
\]
Now, we'll solve for \( x \):
1. Divide both sides of the equation by 27.50 to isolate \( x \):
\[
x = \frac{100}{27.50}
\]
2. Perform the division:
\[
x \approx 3.6363...
\]
Since Dezeree cannot buy a fraction of a sweater, we need to round down to the nearest whole number. Therefore, the maximum number of sweaters she can buy is:
\[
x = 3
\]
Now, we can check if buying 3 sweaters will indeed allow her to spend exactly $100:
- Cost for 3 sweaters:
\[
3 \times 27.50 = 82.50
\]
Dezeree would spend $82.50, and she would have money left over:
\[
100 - 82.50 = 17.50
\]
Next, we check if she can buy 4 sweaters:
- Cost for 4 sweaters:
\[
4 \times 27.50 = 110.00
\]
Since $110 exceeds the $100 gift card balance, she cannot buy 4 sweaters.
Thus, the solution is valid, and Dezeree can buy a maximum of **3 sweaters**. This is indeed a viable solution, as it stays within her budget of $100.