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 hundred solve it and determine it's a value is a viable solution

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.