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Here's your shmoop du jour...

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If 2A + 5B = 48,

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3A + 4C = 47,

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and 2B + 2C = 22, then what is A - B - C?

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And here are the potential answers...

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Okay, so we have 3 equations and 3 variables.

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We can start by isolating A in the first two equations.

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We subtract 5B and divide by 2 for the first equation... which gives us A = (48 - 5B)/2

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For the second equation, we can subtract 4C from both sides, and divide by 3.

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And that gives us A = 47 - 4C over 3.

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Now we set the two equations equal to each other and multiply both sides by 6.

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We can distribute into both parentheses, to get 144 - 15B = 94 - 8C.

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We still have 2 variables, and haven't touched our final equation.

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First, we can divide both sides by 2 to simplify the equation.

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Then, we subtract C from both sides to get B = 11 - C.

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Now we plug B into our earlier equation to get 144 - 15(11 - C) = 94 - 8C.

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Now it's simply a matter of distributing and then combining like terms.

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C equals 5. Now that we've solved for C, we can plug it

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back into our previous equations to find the other variables.

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B = 11 - C, and C = 5.

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So B must be 6. For A, we can solve 2A + 5B = 48.

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A equals 9.

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Now that we know all of the values of A, B, and C, we can easily find A - B - C

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is 9 - 6 - 5 which is... -2.

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And our answer is (A).

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