Question

Deserve relieved 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

Answer 1

To determine how many sweaters Deserve can buy with her $100 gift card, we can set up an equation using \( x \) to represent the number of sweaters she can buy.

The cost per sweater is $27.50, so the equation that represents the total expense is:

\[
27.50x = 100
\]

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:

\[
x = 3.63636...
\]

Since the number of sweaters must be a whole number, we need to round down because Deserve cannot buy a fraction of a sweater. Thus, the maximum number of sweaters Deserve can buy is 3.

Next, we can check the total cost if she buys 3 sweaters:

\[
3 \times 27.50 = 82.50
\]

This leaves her with:

\[
100 - 82.50 = 17.50
\]

If she tries to buy 4 sweaters:

\[
4 \times 27.50 = 110
\]

This total exceeds her gift card amount of $100, so buying 4 sweaters is not a viable solution.

Thus, the only viable solution is that Deserve can buy **3 sweaters** for a total of **$82.50**.