Dezeree received a \( \$ 100 \) gift card and needs new sweaters for school. The sweaters cost \( \$ 2750 \) each. Write an equation to determine how many sweaters she can buy and spend exactly \( \$ 100 \). Then solve the equation. Lasily, determine if that solution makes sense in this problem. ( 4 points)

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 \( \$ 2750 \). Therefore, the total cost for \( x \) sweaters is \( 2750x \). We want to find out how many sweaters she can buy such that the total cost equals her gift card amount: \[ 2750x = 100 \] Now, we can solve for \( x \): \[ x = \frac{100}{2750} \] Calculating the right side: \[ x = \frac{100}{2750} = \frac{1}{27.5} \approx 0.03636 \] Since \( x \) represents the number of sweaters, it must be a whole number. The solution \( x \approx 0.03636 \) indicates that Dezeree cannot buy even one sweater with her \( \$ 100 \) gift card, as the cost of a single sweater is significantly higher than her available funds. Thus, the solution makes sense in this context: Dezeree cannot afford any sweaters with her \( \$ 100 \) gift card since each sweater costs \( \$ 2750 \).