Question

Daisy received a $100 gift card and needs new sweaters for fall. The sweaters cost $28.50 each.

Write an equation, then solve the equation to determine how many sweaters she can buy.

Answer 1

To determine how many sweaters Daisy can buy with her $100 gift card, we can start by defining a variable:

Let \( x \) be the number of sweaters Daisy can buy.

The cost of each sweater is $28.50. Therefore, the total cost for \( x \) sweaters is \( 28.50x \).

Since she has $100 to spend, we can write the equation:

\[
28.50x \leq 100
\]

Next, we solve the equation for \( x \):

1. Divide both sides of the inequality by 28.50:

\[
x \leq \frac{100}{28.50}
\]

2. Calculate the right side:

\[
x \leq 3.50877 \ldots
\]

Since Daisy cannot buy a fraction of a sweater, we take the floor of this number:

\[
x \leq 3
\]

Thus, the maximum whole number of sweaters Daisy can buy is 3.

To verify, we can check the total cost for 3 sweaters:

\[
28.50 \times 3 = 85.50
\]

This cost is under $100, allowing her to buy 3 sweaters.

If we check for 4 sweaters:

\[
28.50 \times 4 = 114.00
\]

This exceeds her gift card amount.

Therefore, the maximum number of sweaters Daisy can buy is

\[
\boxed{3}
\]