If your income is [tex]$820[/tex] a month and you plan to budget [tex]\frac{1}{2}[/tex] of your income for rent and [tex]\frac{3}{10}[/tex] of your income for food, how much do you plan to spend each month on these two items? Simplify your answer.
Certainly! Let's go through the problem step by step.
Step 1: Determine the monthly income. - The monthly income is given as [tex]$820.
Step 2: Calculate the amount to be spent on rent.
- You plan to spend \(\frac{1}{2}\) of your income on rent.
- To find the amount to be spent on rent:
\[
\text{Rent Amount} = \frac{1}{2} \times 820 = 410
\]
Step 3: Calculate the amount to be spent on food.
- You plan to spend \(\frac{3}{10}\) of your income on food.
- To find the amount to be spent on food:
\[
\text{Food Amount} = \frac{3}{10} \times 820 = 246
\]
Step 4: Calculate the total amount planned to be spent on rent and food.
- To find the total amount planned to be spent on both rent and food:
\[
\text{Total Amount} = \text{Rent Amount} + \text{Food Amount} = 410 + 246 = 656
\]
Summary:
- You plan to spend $[/tex]410 on rent each month. - You plan to spend [tex]$246 on food each month.
- The total amount you plan to spend each month on rent and food is $[/tex]656.
These calculations show how you distribute your monthly income of $820 between rent and food.
