Dezeree received a $100 gift card and needs new sweaters for school. The sweaters cost $27.50 each. Write an equation to determine how many sweaters she can buy and spend exactly $100, solve it, and determine if the value is a viable solution. Is the solution viable?

Answer 1

To determine how many sweaters Dezeree can buy with her $100 gift card, we need to set up an equation. Let \( x \) represent the number of sweaters she buys. Each sweater costs $27.50, so the equation to represent her total spending is:

\[ 27.50x = 100 \]

Now, we will solve for \( x \):

1. Divide both sides of the equation by 27.50:

\[ x = \frac{100}{27.50} \]

2. Perform the division:

\[ x \approx 3.63636 \]

Since Dezeree can only buy a whole number of sweaters, we need to evaluate if she can buy exactly 3 or 4 sweaters.

• If she buys 3 sweaters:

\[ 27.50 \times 3 = 82.50 \quad \text{(total cost)} \]

• If she buys 4 sweaters:

\[ 27.50 \times 4 = 110.00 \quad \text{(total cost)} \]

Now, we can see that:

• Buying 3 sweaters costs $82.50, which is within her budget of $100.
• Buying 4 sweaters costs $110.00, which exceeds her budget of $100.

Thus, the maximum whole number of sweaters Dezeree can buy without exceeding her budget is 3.

Conclusion:

The solution to the equation \( 27.50x = 100 \) shows that \( x \approx 3.64 \) is not a viable solution since she cannot purchase a fraction of a sweater. However, she can viably purchase 3 sweaters, spending $82.50, while staying within her budget of $100.