Sure, let's solve the problem step-by-step.
1. Initial Expenses:
- Car-gas: [tex]$\$[/tex]250[tex]$
- Insurance: $[/tex]\[tex]$150$[/tex]
- Food: [tex]$\$[/tex]120[tex]$
- Clothes: $[/tex]\[tex]$300$[/tex]
- College Savings: [tex]$\$[/tex]75[tex]$
- Recreation: $[/tex]\[tex]$25$[/tex]
2. Wages:
- Wages_1: [tex]$\$[/tex]1050[tex]$
- Wages_2: $[/tex]\[tex]$775$[/tex]
3. Net Income:
- Net Income: [tex]$\$[/tex]130[tex]$
4. Expense Reductions:
- Reduce college savings by \$[/tex]50: [tex]$\$[/tex]75 - \[tex]$50 = \$[/tex]25[tex]$
- Reduce clothes expense by \$[/tex]75: [tex]$\$[/tex]300 - \[tex]$75 = \$[/tex]225[tex]$
- Reduce recreation expense by \$[/tex]25: [tex]$\$[/tex]25 - \[tex]$25 = \$[/tex]0[tex]$
5. Updated Expenses:
After applying the reductions, the new values are:
- Car-gas: $[/tex]\[tex]$250$[/tex]
- Insurance: [tex]$\$[/tex]150[tex]$
- Food: $[/tex]\[tex]$120$[/tex]
- Clothes: [tex]$\$[/tex]225[tex]$
- College Savings: $[/tex]\[tex]$25$[/tex]
- Recreation: [tex]$\$[/tex]0[tex]$
6. Total Updated Expenses:
- For Wages_1:
Every expense category matters:
\[
\text{Total Expenses}_1 = \$[/tex]250 + \[tex]$150 + \$[/tex]120 + \[tex]$225 + \$[/tex]25 + \[tex]$0 = \$[/tex]770
\]
- For Wages_2:
Recreation is not included:
[tex]\[
\text{Total Expenses}_2 = \$250 + \$150 + \$120 + \$225 + \$25 = \$770
\][/tex]
7. Updated Net Income:
- For Wages_1:
[tex]\[
\text{Net Income}_1 \text{ updated} = \$1050 - \$770 = \$280
\][/tex]
- For Wages_2:
[tex]\[
\text{Net Income}_2 \text{ updated} = \$775 - \$770 = \$5
\][/tex]
8. Summary of Updated Values:
- College Savings: [tex]$\$[/tex]25[tex]$
- Clothes: $[/tex]\[tex]$225$[/tex]
- Recreation: [tex]$\$[/tex]0[tex]$
- Total Expenses for Wages_1: $[/tex]\[tex]$770$[/tex]
- Total Expenses for Wages_2: [tex]$\$[/tex]770[tex]$
- Updated Net Income for Wages_1: $[/tex]\[tex]$280$[/tex]
- Updated Net Income for Wages_2: [tex]$\$[/tex]5$
Hence, these are the updated expenses and net incomes after the reductions.
