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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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DizzyBerco

Answer:

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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