Tom,Ted,Tony,Terry worked together on a job.The job paid $500.Each boy was paid according to the amount of work he contributed to the job.Ted and Tony earned $280 together.Ted and Tom have $260,and Ted and Terry got $220.What percent of the job did each boy do?
What part of Bobpursley's answer don't you understand?
http://www.jiskha.com/display.cgi?id=1257801021
everything
To determine the percentage of the job each boy did, we need to find their individual contributions relative to the total job.
Let's represent the percent of the job each boy did as follows:
Tom's share: T%
Ted's share: E%
Tony's share: O%
Terry's share: Y%
We have the following information:
1) Ted and Tony earned $280 together: E% + O% = $280
2) Ted and Tom earned $260 together: E% + T% = $260
3) Ted and Terry earned $220 together: E% + Y% = $220
We also know that the total job paid $500:
T% + E% + O% + Y% = $500
To solve this system of equations, we can use substitution.
From equation 2, we can rewrite it as T% = $260 - E%.
From equation 3, we can rewrite it as Y% = $220 - E%.
Substituting these values into the total job equation, we get:
($260 - E%) + E% + O% + ($220 - E%) = $500
Simplifying the equation, we have:
$480 - E% + O% = $500
O% - E% = $20
From equation 1, we know that E% + O% = $280.
Substituting this into the previous equation, we get:
$280 - E% - E% = $20
2E% = $280 - $20
2E% = $260
Dividing both sides by 2, we find:
E% = $260 / 2
E% = 130
Now we can substitute this value into the other equations to find the percentages of the other boys.
From equation 2, we have:
T% + 130% = $260
T% = $260 - 130%
T% = $130
From equation 3, we have:
Y% + 130% = $220
Y% = $220 - 130%
Y% = $90
Finally, to find Tony's percentage (O%), we can use equation 1:
130% + O% = $280
O% = $280 - 130%
O% = $150
So, the percentage of the job each boy did is as follows:
Tom: 130%
Ted: 130%
Tony: 150%
Terry: 90%