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.

Answer 1

To determine how many pairs of pants Dezeree can buy and spend exactly $200, you can set up the equation as follows:

Let \( x \) be the number of pairs of pants Dezeree buys. Each pair of pants costs $32.50, so the total cost for the pants will be \( 32.50x \).

Since she wants to spend exactly $200, we can set up the equation:

\[ 32.50x = 200 \]

Now, let's solve for \( x \):

1. Divide both sides of the equation by 32.50:

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

2. Calculate the right side:

\[ x = 200 \div 32.50 = 6.15384615384 \]

Since \( x \) represents the number of pairs of pants, it must be a whole number. Thus, we round down since Dezeree can only buy whole pairs of pants.

The maximum whole number of pairs she can buy is \( 6 \).

Now, let's calculate how much money she would spend if she buys 6 pairs of pants:

\[ 32.50 \times 6 = 195 \]

This means she would spend $195, and she would have:

\[ 200 - 195 = 5 \]

So, if she buys 6 pairs of pants, she will have $5 left over.

If she tries to buy 7 pairs of pants:

\[ 32.50 \times 7 = 227.50 \]

This amount exceeds $200, which means it’s not a viable option.

Conclusion

The maximum number of pairs of pants Dezeree can buy while spending exactly $200 is 6 pairs, allowing her to spend $195 and have $5 left over.