A family spends 20% of its monthly income on food, 23% on rent, and 42% on other expenses and saves the balance. If the family saves $360 per month, is their monthly income $2,400?

Yes. You're right. The family's monthly income is $2400.

To find out if the family's monthly income is $2,400, we need to first calculate the total percentage of income spent on food, rent, and other expenses.

Let's start by calculating the total percentage of income spent:

Food: 20%
Rent: 23%
Other expenses: 42%

To find the percentage of money saved, subtract the sum of these percentages from 100%:

100% - (20% + 23% + 42%) = 100% - 85% = 15%

We know that the family saves 15% of its monthly income, which amounts to $360. Now, we can calculate the total monthly income.

Let X be the total monthly income.
15% of X = $360

To find X, we need to divide the savings by the saving percentage (15%):

X = $360 / 0.15 = $2400

Therefore, the family's monthly income is indeed $2,400.