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10 January, 15:43

2. Four devices (A, B, C, D) contain a total 225GB of data. - The device A has half as much data as device B. - The device C has five times as much data as device B and device D combined. - The sum of twice the amount of data on device C and four times the amount of data on the device D is equal to the difference between 500GB and the amount of data on device B. Determine the amount of data (in GB) on each device.

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  1. 10 January, 17:37
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    A = 3 GB

    B = 6 GB

    C = 185 GB

    D = 31 GB

    Step-by-step explanation:

    First off, we need to find all of our equations.

    A + B + C + D = 225

    B = 2A (2A because we know that A is half of B)

    C = 5 (B+D)

    2C + 4D = 500 - B or B + 2C + 4D = 500

    Now we can eliminate B by substituting it to 2A.

    A + 2A + C + D = 225

    3A + C + D = 225 (1st Equation)

    C = 5 (2A + D)

    C = 10A + 5D (2nd Equation)

    2A + 2C + 4D = 500 (3rd Equation)

    Now let's eliminate C by substituting it to the first equation and the third equation.

    3A + 10A + 5D + D = 225

    13A + 6D = 225

    2A + 2 (10A + 5D) + 4D = 500

    2A + 20A + 10D + 4D = 500

    22A + 14D = 500

    Now we are left with two equations:

    13A + 6D = 225

    22A + 14D = 500

    We can eliminate A or D by using the multiply first method.

    -7 (13A + 6D = 225)

    3 (22A + 14D = 500)

    -91A - 42D = - 1575

    66A + 42D = 1500

    -25A = - 75

    Divide both sides by - 25 to find for A.

    A = 3

    Now that we know A = 3, we can also solve for the value of D.

    66A + 42D = 1500

    66 (3) + 42D = 1500

    198 + 42D = 1500

    42D = 1500 - 198

    D = 31

    Now that we have the value of A, we can also solve for B.

    B = 2A

    B = 2 (3)

    B = 6

    Now that we have the value of A and D, we can solve for C.

    C = 10A + 5D

    C = 10 (3) + 5 (31)

    C = 30 + 155

    C = 185

    So in conclusion each drive has:

    A = 3 GB

    B = 6 GB

    C = 185 GB

    D = 31 GB

    The final check would be to use out very first equation.

    A + B + C + D = 225

    3 + 6 + 185 + 31 = 225

    225 = 225
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