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.pllzz

Answer 1

To determine how many sweaters Dezeree can buy with a $100 gift card where each sweater costs $27.50, we can set up the following equation:

Let \( x \) be the number of sweaters Dezeree can buy. The total cost of the sweaters can be expressed as:

\[ 27.50x = 100 \]

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

1. Divide both sides by 27.50:

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

2. Calculate the right side:

\[ x = \frac{100}{27.50} = 3.63636363636 \]

Since Dezeree cannot buy a fraction of a sweater, we round down to the nearest whole number. Thus, she can buy 3 sweaters.

To determine the total cost for 3 sweaters:

\[ \text{Total cost} = 27.50 \times 3 = 82.50 \]

Since \( 82.50 \) is less than \( 100 \), Dezeree still has some money left on her gift card.

Now, if we check the number of sweaters she could buy if she rounded up to 4:

\[ \text{Cost for 4 sweaters} = 27.50 \times 4 = 110 \]

This exceeds her $100 budget.

Conclusion

Dezeree can buy a maximum of 3 sweaters, which totals $82.50, and she will have $17.50 left on her gift card. Thus, the viable solution is that she can buy 3 sweaters.