Chris, Ed, and Paul decide to help each other by doing repairs on each ofher's houses. Chris is a carpenter, Ed is an electrician, and Paul is a plumber. Each does work on his own house as well as ou the others houses. When they are all finished they realize that Chris spent $30\%$ of his fime on his own house, $40\%$ of his time on Ed's house, and $30\%$ on Paul's house, Ed spent half of his time on his own house, $30\%$ on Chris house, and remaining on Paul's house. Paul spent $40\%$ of the time on his own house, $40\%$ on Chris' house, and $20\%$ on Ed's house. If they originally agreed that each should get about a $\$2300$ for their work, how much money should each get for their work?

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Grade 6

One-step inequalities: word problems

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Q. Chris, Ed, and Paul decide to help each other by doing repairs on each ofher's houses. Chris is a carpenter, Ed is an electrician, and Paul is a plumber. Each does work on his own house as well as ou the others houses. When they are all finished they realize that Chris spent

30\%

of his fime on his own house,

40\%

of his time on Ed's house, and

30\%

on Paul's house, Ed spent half of his time on his own house,

30\%

on Chris house, and remaining on Paul's house. Paul spent

40\%

of the time on his own house,

40\%

on Chris' house, and

20\%

on Ed's house. If they originally agreed that each should get about a

\$2300

for their work, how much money should each get for their work?

Calculate Percentage Time: Calculate the percentage of time Ed spent on Paul's house. Since Ed spent $50\%$ on his own house and $30\%$ on Chris's house, the remaining time on Paul's house is $100\% - (50\% + 30\%) = 20\%$ .
Check Total Percentage: Check the total percentage of time each spent on all houses to ensure it sums to $100\%$ . Chris: $30\% + 40\% + 30\% = 100\%$ , Ed: $50\% + 30\% + 20\% = 100\%$ , Paul: $40\% + 40\% + 20\% = 100\%$ .
Equal Work Value: Since each person's work is valued equally at $\$2300$ , and they spent equal time on each other's houses as per the percentages, each should receive $\$2300$ for their work.