## MTH062 Quantitative Literacy 1Math for "Real" Life

### Systems Equations

Solve for x and y:
-x+3y=-4
-3x-4y=27

Choose a variable to eliminate. Eliminate x first. Multiply equation 1 by -3:
-3*(-x+3y=-4)
-3x-4y=27

Distribute:
3x-9y=12
-3x-4y=27

-13y=39

Solve for y:
y=39/-13=-3

Substitute into one of the equations and solve for x:
-x+3(-3)=-4
-x-9=-4
-x-9+9=-4+9
-x=5
x=-5

We think the solution is (-5,-3).

CHECK:
Plug both values into the other equation to check:
-3(-5)-4(-3)=15+12=27
It checks!!!

### § 1-2 Eighteen Trillion and Counting

Problem situation: How Big Is a Billion or a Trillion?

So, where on the number line is 1 billion? Make a mark for 1 billion on the number line.

In news about politics and government, BIG numbers are talked about often. Below is a chart showing the national deficit over time.

On a scale from 0 to 1 trillion, 1 billion is very close to zero, since 1 trillion is 1000 billion!

Imagine a stack of 1,000 one‐dollar bills, which is about 4.3 inches tall.
Complete the table below:

$Amount Height (inches) Height (feet) Height (miles)$1,000 4.3
$1 million 4,300 358$1 billion 4,300,000 358,333 68
$1 trillion 4,300,000,000 358,333,333 68,866 This means that a stack of$1 bills, 3.5 trillion high, would reach the moon.

### Polynomial Division

(x^3-3x^2+4x-5)/(x-2)

Use long division to find the quotient and remainder:
x-2 \ bar(")"\ x^3-3x^2+4x-5)

What do you multiply by x to get x^3?
Guess: x^2 and multiply:

 x^2 x-2 )x^3 -3x^2 +4x -5 x^3 -2x^2

Now subtract:

 x^2 x-2 ) x^3 -3x^2 +4x -5 -(x^3 -2x^2) -1x^2 +4x

What would you multiply by x to get -1x^2?

Guess: -1x and multiply.

 x^2 -1x x-2 ) x^3 -3x^2 +4x -5 -(x^3 -2x^2) -1x^2 +4x -1x^2 +2x

Now subtract:

 x^2 -1x x-2 ) x^3 -3x^2 +4x -5 -(x^3 -2x^2) -1x^2 +4x -( -1x^2 +2x) 2x -5

What would you multiply by x to get 2x?

Guess: 2 and multiply.

 x^2 -1x +2 x-2 ) x^3 -3x^2 +4x -5 -(x^3 -2x^2) -1x^2 +4x -( -1x^2 +2x) 2x -5 2x -4

Now subtract.

 x^2 -1x +2 x-2 ) x^3 -3x^2 +4x -5 -(x^3 -2x^2) -1x^2 +4x -( -1x^2 +2x) 2x -5 -( 2x -4) -1

Solution: (x^3-3x^2+4x-5)/(x-2)=x^2-x+2+(-1)/(x-2)

CHECK:
(x-2)(x^2-x+2)-1=x^3-3x^2+4x-5 check.

### § 2-1 A Taxing Set of Problems

Problem Situation: Calculate income tax for tax bracket

If Taxable Income Is: The Tax Is:
Not over $18,150 10% of the taxable income Over$18,150 but not over $73,800$1,815 plus 15% of the excess over $18,150 Over$73,800 but not over 148,850 $10,162.50 plus 25% of the excess over$73,800

Suppose a couple, married with no kids, filing jointly, earned $93,000 with no other interest or income. Based on the standard standard married filing jointly deduction, their taxable income is $93,000-$20,300=$72,700

According to the tax table above their income tax is
$1,815+0.15*($72,700-$18,150)=$9,997.50

Compare this to line 15 of the table below:

##### Disclaimer:

You should check with your advisor before taking a math class leading to calculus. Algebra classes are known to cause stress, anger, depression, and occasionally rashes, as well as lead to calculus. Please consult a physician if negative symptoms persist.