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.

Question

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Answer 1

To determine how many sweaters Dezeree can buy with her $100 gift card, we can set up the following equation:

Let \( x \) be the number of sweaters Dezeree can buy. The cost of each sweater is $27.50, and she wants to spend exactly $100.

The equation can be written as:

\[ 27.50x = 100 \]

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

1. Divide both sides of the equation by 27.50:

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

2. Calculate the right side:

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

The value of \( x \) is approximately \( 3.64 \).

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

Now, we can verify this:

1. If she buys 3 sweaters, the total cost would be:

\[ 3 \times 27.50 = 82.50 \]

2. If she attempts to buy 4 sweaters, the total cost would be:

\[ 4 \times 27.50 = 110.00 \]

Since $110.00 is over $100, she cannot buy 4 sweaters.

Therefore, the maximum number of whole sweaters Dezeree can buy is 3 sweaters for a total of $82.50, which is a viable solution. She will have some money left over from her gift card ($17.50).