An architect spends 15% of her monthly income on office rent and 10% on software subscriptions. She deposits $3,600 into a retirement account and saves 5x% of her income. If her total monthly income is $12,000, what is the value of x?

The correct answer is 9.

To find the value of x, we break down how the total monthly income of $12,000 is distributed across expenditures and savings:
- Office rent: 15% of monthly income
- Software subscriptions: 10% of monthly income
- Retirement account deposit: $3,600
- Savings: 5x% of monthly income

First, calculate the percentage of total income represented by the $3,600 retirement deposit:

$\text{Retirement Percentage}=\frac{3600}{12000}\times 100\%=30\%$

Next, sum all the percentage allocations of monthly income, which must equal 100%:

$15\%+10\%+30\%+5\mathrm{x<mo>\%</mo><mo>=</mo><mn>100</mn><mo>\%</mo>}$

Combine the known percentage values:

$55\%+5\mathrm{x<mo>\%</mo><mo>=</mo><mn>100</mn><mo>\%</mo>}$

Subtract 55% from both sides to find the savings percentage:

$5x=45$

Divide both sides by 5 to solve for x:

$x=\frac{45}{5}=9$

Thus, the value of x is 9.