Dezeree received a $200 gift card and needs new pants for school. The pants cost $32.50 each. Write an equation to determine how many sweaters she can buy and spend exactly $200, Solve it and determine if the value is a viable solution.

Question

The equation to represent this situation is . After you solve p= . This is because

Answer 1

To determine how many pairs of pants Dezeree can buy with her $200 gift card, we can create an equation based on the cost of the pants.

Let \( p \) represent the number of pants Dezeree can buy. Each pair of pants costs $32.50. We can write the equation for the total spending as follows:

\[ 32.50p = 200 \]

Now, we'll solve for \( p \):

1. Divide both sides of the equation by 32.50:

\[ p = \frac{200}{32.50} \]

2. Calculate the right side:

\[ p = \frac{200}{32.50} = 6.1538 \ldots \]

Since Dezeree cannot buy a fraction of a pair of pants, we round down the value of \( p \) to the nearest whole number. Therefore, the maximum number of pairs of pants she can buy is:

\[ p = 6 \]

To confirm:

3. Calculate the total cost if she buys 6 pairs:

\[ \text{Total Cost} = 32.50 \times 6 = 195 \]

If she attempted to buy 7 pairs:

4. Calculate the total cost for 7 pairs:

\[ \text{Total Cost} = 32.50 \times 7 = 227.50 \]

Since $227.50 exceeds her $200 budget, she cannot buy 7 pairs.

Conclusion

The equation to represent this situation is \( 32.50p = 200 \). After solving, \( p = 6 \).

This is because with 6 pairs of pants, she spends $195, which is within her budget of $200. Thus, 6 is a viable solution. She cannot buy 7 pairs because that cost exceeds her gift card.