i don't get it ....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? HELP.......
As far as I can see, you've made no attempt to solve this problem yourself, or to follow Bob's instructions.
If you post what you do know about this problem, we'll be glad to help you from there.
Let's break down the given information step-by-step:
1. Ted and Tony earned $280 together.
2. Ted and Tom earned $260 together.
3. Ted and Terry earned $220 together.
To find out the percentage of the job each boy did, we need to determine the individual earnings of each boy.
Let's assign variables for each person's earnings:
- Let's say Ted's earnings are T.
- Tony's earnings will be A.
- Tom's earnings will be O.
- Terry's earnings will be Y.
From the given information, we can create the following equations:
From statement 1:
T + A = 280
From statement 2:
T + O = 260
From statement 3:
T + Y = 220
Now, let's solve these equations step-by-step to find the values of each variable.
Step 1:
Subtract equation 2 from equation 1 to eliminate T, which gives:
(A - O) = 20 [equation 4]
Step 2:
Subtract equation 2 from equation 3 to eliminate T, which gives:
(Y - O) = -40 [equation 5]
Now we have two equations (equation 4 and equation 5) and two variables (A and O). We can solve these equations simultaneously to find the values of A and O.
Step 3:
Adding equation 4 to equation 5 eliminates the variable O:
(A - O) + (Y - O) = 20 + (-40)
A + Y - 2O = -20 [equation 6]
Step 4:
Substitute the value of (A - O) from equation 4 into equation 6:
20 + Y - 2O = -20
Y - 2O = -40 [equation 7]
Step 5:
Rearrange equation 6 to solve for A:
A = -20 - Y + 2O [equation 8]
Step 6:
Substitute the value of A from equation 8 into equation 1:
T + (-20 - Y + 2O) = 280
T - Y + 2O = 300 [equation 9]
Step 7:
Substitute the value of A from equation 8 into equation 3:
T + (-20 - Y + 2O) = 220
T - Y + 2O = 240 [equation 10]
Now we have two equations (equation 9 and equation 10) and two variables (T and O). We can solve these equations simultaneously to find the values of T and O.
Step 8:
Subtract equation 10 from equation 9 to eliminate (T - Y), which gives:
(O - 240) - (O - 300) = 0
60 = 0
From this step, we can conclude that there is no solution to the system of equations. This means there is no consistent solution for the earnings of each person given the information provided.
Therefore, we cannot determine the exact percentage of the job each boy did with the given information.
To solve this problem, we need to figure out the percentage of work done by each boy by comparing the amounts they earned. Here's how we can approach it step by step:
1. Let's assume that the work contributed by Tom, Ted, Tony, and Terry are represented by variables t, e, o, and r, respectively.
2. Based on the given information, we can create three equations:
- Ted + Tony = $280 (Equation 1)
- Ted + Tom = $260 (Equation 2)
- Ted + Terry = $220 (Equation 3)
3. From Equation 1, we can substitute Ted with (280 - Tony) and rewrite Equation 2:
(280 - Tony) + Tom = $260
4. Similarly, we can substitute Ted with (220 - Terry) in Equation 2:
(220 - Terry) + Tom = $260
5. Now we have two equations (Equation 2 and the modified Equation 2) with two variables (Tom and Terry). We can solve these equations simultaneously to find the values of Tom and Terry.
6. Subtracting the modified Equation 2 from Equation 2, we get:
Tom - (220 - Terry) = 260 - 220
Simplifying:
Tom - 220 + Terry = 40
Tom + Terry = 260
7. We know from Equation 1 that Tony + Ted = 280. By rearranging, we have:
Tony = 280 - Ted
8. Since Ted = 220 - Terry (from Equation 3), we can substitute Ted in terms of Terry into the equation Tony = 280 - Ted:
Tony = 280 - (220 - Terry)
Tony = 280 - 220 + Terry
Tony = 60 + Terry
9. Substituting the value of Tony into the Equation 1, we get:
(220 - Terry) + (60 + Terry) = 280
Solving for Terry:
220 - Terry + 60 + Terry = 280
280 + 60 - 220 = Terry + Terry
120 = 2Terry
Terry = 60
10. Now that we have found the value of Terry, we can substitute it into either Equation 2 or the modified Equation 2 to find Tom's value:
(220 - Terry) + Tom = 260
220 - 60 + Tom = 260
Tom = 260 - 220 + 60
Tom = 100
11. Now that we have the values of Tom and Terry, we can find the values of Ted and Tony using Equation 1:
Ted + Tony = 280
Ted + (60 + Terry) = 280
Ted + 60 + 60 = 280
Ted = 280 - 120
Ted = 160
12. Finally, we can calculate the percentage of work done by each boy by dividing their respective contributions by the total work:
Percentage of work done by Tom = (Tom's work / Total work) * 100
= (100 / 500) * 100
= 20%
Percentage of work done by Ted = (Ted's work / Total work) * 100
= (160 / 500) * 100
= 32%
Percentage of work done by Tony = (Tony's work / Total work) * 100
= (60 / 500) * 100
= 12%
Percentage of work done by Terry = (Terry's work / Total work) * 100
= (60 / 500) * 100
= 12%
Therefore, Tom did 20% of the job, Ted did 32% of the job, Tony did 12% of the job, and Terry did 12% of the job.