Solve for Male Gift Costs: 1/(4+a) and (a-2)/3 Fraction Problem

To solve this problem, we'll proceed as follows:

• Step 1: Address the known values and set up the equation. The cost for females is $\frac{a-2}{3}$ dollars.
• Step 2: Calculate the discount Monica receives, which is twice the spending on females: $2 \times \frac{a-2}{3} = \frac{2(a-2)}{3}$ dollars.
• Step 3: Write the equation for total spending:
  $\frac{1}{4+a} + \frac{a-2}{3} - \frac{2(a-2)}{3} = 2 - \frac{a}{3}$.
• Step 4: Simplify the equation for clarity:

The spending on females is $\frac{a-2}{3}$, and the discount is $\frac{2(a-2)}{3}$.
The net spending results in the equation:
$\frac{1}{4+a} + \frac{a-2}{3} - \frac{2(a-2)}{3} = 2 - \frac{a}{3}$
Simplifying:
$\frac{1}{4+a} + \frac{a-2}{3} - \frac{2a - 4}{3} = 2 - \frac{a}{3}$
$\frac{1}{4+a} + \cancel{\frac{a-2}{3}} - \cancel{\frac{2a-4}{3}} = 2 - \frac{a}{3}$

The left side becomes
$\frac{1}{4+a} = 2 - \frac{a}{3}$

Rearranging terms to solve for the cost spent on males, we notice an inconsistency leading all terms to not hold realistic buying conditions. Thus:

• There is no logical or feasible value that satisfies practical non-negative spending on females.

Therefore, the solution to the problem is that it is not possible because she bought gifts costing a negative value.