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Algebra and Functions Videos 140 videos

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SAT Math 7.5 Algebra and Functions 197 Views


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Description:

SAT Math 7.5 Algebra and Functions

Language:
English Language

Transcript

00:02

Here's your shmoop du jour...

00:04

If 2A + 5B = 48,

00:07

3A + 4C = 47,

00:10

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

00:15

And here are the potential answers...

00:18

Okay, so we have 3 equations and 3 variables.

00:23

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

00:27

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

00:37

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

00:42

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

00:46

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

00:52

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

01:00

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

01:03

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

01:07

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

01:13

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

01:20

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

01:25

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

01:29

back into our previous equations to find the other variables.

01:32

B = 11 - C, and C = 5.

01:36

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

01:46

A equals 9.

01:48

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

01:53

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

01:56

And our answer is (A).

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