To find out how many sweaters Dezeree can buy with her $100 gift card, we can start by setting up the equation. Let \( x \) be the number of sweaters she can buy.
The cost of each sweater is $27.50. The total cost for \( x \) sweaters will be \( 27.50x \). We want this total cost to equal $100. Therefore, we can write the equation as:
\[ 27.50x = 100 \]
Now, let's solve for \( x \):
- Divide both sides of the equation by 27.50:
\[ x = \frac{100}{27.50} \]
- Calculate the right side:
\[ x \approx 3.6364 \]
Since Dezeree cannot buy a fraction of a sweater, we need to round down to the nearest whole number, which means Dezeree can buy 3 sweaters.
To check whether this value is viable, we can calculate the total cost of 3 sweaters:
\[ \text{Total cost for 3 sweaters} = 27.50 \times 3 = 82.50 \]
This is under $100, so it is a viable solution.
If we also check the next whole number (4 sweaters):
\[ \text{Total cost for 4 sweaters} = 27.50 \times 4 = 110.00 \]
This exceeds her $100 budget, confirming that purchasing 4 sweaters is not viable.
Summary
The equation is \( 27.50x = 100 \), and the solution is \( x = 3 \) sweaters. This allows Dezeree to spend $82.50, which is a viable amount within her $100 budget.