Problem 58 - Basic College Mathematics

Question

A family has an annual income of \(\$ 28,140 .\) Of this, \(\frac{1}{5}\) is spent for food, \(\frac{1}{4}\) for housing, \(\frac{1}{10}\) for clothing, \(\frac{1}{14}\) for savings, \(\frac{1}{5}\) for taxes, and the rest for other expenses. How much is spent for each?

Step-by-Step Solution

Answer

Foods: \$5628\, Housing: \$7035\, Clothing: \$2814\, Savings: \$2010\, Taxes: \$5628\, Other expenses: \$5025\.

Step 1 - Determine the amount spent on food

To find out how much is spent on food, calculate \( \frac{1}{5} \) of the annual income: \[ \frac{1}{5} \times 28140 = 5628 \] So, the amount spent on food is \$5628\.

Step 2 - Determine the amount spent on housing

To find out how much is spent on housing, calculate \( \frac{1}{4} \) of the annual income: \[ \frac{1}{4} \times 28140 = 7035 \] So, the amount spent on housing is \$7035\.

Step 3 - Determine the amount spent on clothing

To find out how much is spent on clothing, calculate \( \frac{1}{10} \) of the annual income: \[ \frac{1}{10} \times 28140 = 2814 \] So, the amount spent on clothing is \$2814\.

Step 4 - Determine the amount saved

To find out how much is saved, calculate \( \frac{1}{14} \) of the annual income: \[ \frac{1}{14} \times 28140 = 2010 \] So, the amount saved is \$2010\.

Step 5 - Determine the amount spent on taxes

To find out how much is spent on taxes, calculate \( \frac{1}{5} \) of the annual income: \[ \frac{1}{5} \times 28140 = 5628 \] So, the amount spent on taxes is \$5628\.

Step 6 - Determine the amount spent on other expenses

First, add the amounts spent on food, housing, clothing, savings, and taxes: \[ 5628 + 7035 + 2814 + 2010 + 5628 = 23115 \] Then, subtract this total from the annual income to find the amount left for other expenses: \[ 28140 - 23115 = 5025 \] So, the amount spent on other expenses is \$5025\.

Key Concepts

annual income

Annual income is the total amount of money earned by a family or individual in one year. In our exercise, the family’s annual income is \(28,140.
This amount is crucial because it helps to understand how the family allocates their money throughout the year.
Knowing the annual income allows us to perform calculations to determine how much is spent in different categories such as food, housing, and more. It’s basically your financial starting point.
To visualize this, imagine you have \)28,140 to spend or save over the next 12 months—how would you divide it?

fractions in budgeting

Fractions are used in budgeting to allocate income into different parts based on necessity. In this exercise, fractions like \( \frac{1}{5} \), \( \frac{1}{4} \), and so on, are employed to represent portions of the family’s annual income.
For example, \( \frac{1}{5} \) of $28,140 means that this fraction of the annual income goes towards food.
Fractions make it easier to see at a glance what part of the total income is used for each category. To get the exact amount for each category, multiply the total income by the fraction.
Understanding these fractions is key to efficient budgeting.

basic arithmetic operations

Basic arithmetic operations are the foundation of budgeting calculations. They include addition, subtraction, multiplication, and division.
For this exercise, multiplication and addition are primarily used. When calculating how much is spent on food, we multiply the annual income by the fraction for food: \[ \frac{1}{5} \times 28140 = 5628 \].
Addition is used when summing up the expenditures from different categories: \[ 5628 + 7035 + 2814 + 2010 + 5628 = 23115 \].
Subtraction comes into play to determine the remainder of the income, which is used for other expenses after taking out the known expenditures: \[ 28140 - 23115 = 5025 \].

financial literacy

Financial literacy is the knowledge and understanding of financial principles and concepts. It includes knowing how to budget, save, invest, and manage money.
In this exercise, we apply financial literacy by determining how a family spends their annual income in various segments, such as food, housing, clothing, savings, and taxes.
Understanding these concepts helps in making informed financial decisions, ensuring you don't overspend in one category while neglecting others.
It empowers you to plan for the future, manage debt effectively, and achieve financial stability and goals.