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?
To find the percentage of the job that each boy did, we need to determine the amount of work each boy contributed.
Let's assign variables to each person's share of the work:
- Let "x" represent Tom's share of the job.
- Let "y" represent Ted's share of the job.
- Let "z" represent Tony's share of the job.
- Let "w" represent Terry's share of the job.
We can then create a system of equations based on the given information:
1. Ted and Tony earned $280 together:
y + z = 280
2. Ted and Tom earned $260:
y + x = 260
3. Ted and Terry earned $220:
y + w = 220
Since the job paid a total of $500, we also know that:
4. x + y + z + w = 500
Now we can solve this system of equations to find the values of x, y, z, and w.
First, we can substitute equation 2 into equation 1 to eliminate y:
y + x + z = 280
Next, subtract equation 3 from equation 2 to eliminate y:
(y + x) - (y + w) = 260 - 220
x - w = 40
Now, we have two equations:
1. x + z = 280 - y
2. x - w = 40
To solve for x and z, we can use the method of substitution.
Substitute x - w (from equation 2) into equation 1:
(x - w) + z = 280 - y
40 + z = 280 - y
Rearrange the equation:
y + z = 280 - 40
y + z = 240
Since y + z = 280 (from equation 1), we can set up the following equation:
280 = 240
280 - 240 = 0
This means that equation 3 (y + w = 220) is inconsistent with the previous information. Therefore, there is no solution to this system of equations, and we cannot determine the exact percentage of the job that each boy did.
However, we can make some observations based on the available information:
- We know that Ted and Tony together earned $280. If we assume that the job is divided equally among Ted, Tony, and Terry (since we don't have enough information to determine their individual contributions), each of them would have earned approximately $93.33 ($280 divided by 3).
- Tom and Ted together earned $260, suggesting that Tom's contribution was greater than Ted's.
- Ted and Terry earned $220, implying that Terry's contribution was less than Ted's.
But without more information or a consistent system of equations, we cannot determine the exact percentage of the job that each boy did.
Ted+Tony=280
Ted+Tom=260
subtract the second equation from the first
a) Tony-Tom=20
Ted+Terry=220
Ted+Tony+Tom+Terry=500
Subtract a) from the last line
Ted+2Tom+Terry=480
but Ted+terry=220 so subtracting
2Tom=260
I assume you can take it from here.