Say 10600 is divided into positive quantities A, B, C, and D. Use the following information to find the value of D: If you remove A, the average of the other 3 numbers is 1000. If you remove B, the average of the other 3 numbers is 3220. If you remove C, the average of the other 3 numbers is 3180.
We are given that the sum of the four quantities is: \[ A + B + C + D = 10600 \] When A is removed, the sum of the remaining three is \( 3 \times 1000 \): \[ B + C + D = 3000 \] From this, we can find A: \[ A = 10600 - 3000 = 7600 \] When B is removed, the sum of the remaining three is \( 3 \times 3220 \): \[ A + C + D = 9660 \] From this, we find B: \[ B = 10600 - 9660 = 940 \] When C is removed, the sum of the remaining three is \( 3 \times 3180 \): \[ A + B + D = 9540 \] From this, we find C: \[ C = 10600 - 9540 = 1060 \] Finally, use the total sum to find D: \[ D = 10600 - (A + B + C) = 10600 - (7600 + 940 + 1060) \] \[ D = 10600 - 9600 = 1000 \]
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