Dezeree received a $$ 100$ gift card and needs new sweaters for school. The sweaters cost $$ 27.50$

Question

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 Dezeree can buy with her $100 gift card, we can set up the equation based on the cost of the sweaters.

Let $x$ represent the number of sweaters she can buy. The cost for $x$ sweaters is given by the equation:

$$27.50x=100$$

Now, to solve for $x$, we can divide both sides of the equation by 27.50:

$$x=\frac{100}{27.50}$$

Calculating the right-hand side:

$$x=\frac{100}{27.50}\approx 3.63636$$

Since Dezeree can only buy a whole number of sweaters, we round down to the nearest whole number because buying a fraction of a sweater isn't possible; thus, she can buy at most 3 sweaters.

Next, let's check how much money she will spend if she buys 3 sweaters:

$$\text{Total cost for 3 sweaters}=27.50\times 3=82.50$$

Now let's see how much money would be left over:

$$\text{Remaining balance}=100-82.50=17.50$$

Also, let's check if she can buy 4 sweaters:

$$\text{Total cost for 4 sweaters}=27.50\times 4=110.00$$

Since $110.00 exceeds her $100 gift card limit, she cannot buy 4 sweaters.

Thus, the number of sweaters that Dezeree can buy and spend exactly $100 is 3.

In conclusion, the viable solution is:

$$\boxed{{\displaystyle 3}}$$

If fraud was considered, her remaining balance would be $17.50 after purchasing 3 sweaters.

Answer 2

Can you give a shorter answer

Answer 3

Sure!

Let $x$ be the number of sweaters Dezeree can buy. The equation based on the cost is:

$$27.50x=100$$

Solving for $x$:

$$x=\frac{100}{27.50}\approx 3.64$$

Since she can only buy whole sweaters, she can buy 3 sweaters.

Calculating the total cost for 3 sweaters:

$$27.50\times 3=82.50$$

Remaining balance:

$$100-82.50=17.50$$

Thus, Dezeree can buy 3 sweaters.

Final answer: $\boxed{{\displaystyle 3}}$