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.
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