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:

$$p=\frac{200}{32.50}=6.1538\dots$$

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.