MATH

Lesson 2.1

#1 Points possible: 18. Total attempts: 5

Because their situation is pretty simple, this couple can fill out a 1040EZ tax form.  As the name implies, this is the easy form for simple cases.  Fill out the income portion of the form to find the couple's taxable income.

Income Attach Form(s) W-2 here. Enclose, but do not attach, any payment.	1	Wages, salaries, and tips. This should be shown in box 1 of your Form(s) W-2. Attach your Form(s) W-2.	1
	2	Taxable interest. If the total is over $1,500, ou cannot use Form 1040EZ.	2
	3	Unemployment compensation and Alaska Permanent Fund dividends (see instructions)	3
	4	Add lines 1, 2, and 3. This is your adjusted gross income.	4
	5	If someone can claim you (or your spouse if a joint return) as a dependent, check the applicable box(es) below and enter the amount from the worksheet on back. [  ] You      [  ] Spouse If no one can claim you (or your spouse if a joint return), enter $10,150 if single; $20,300 if married filing jointly. See back for explanation.	5
	6	Subtract line 5 from line 4. If line 5 is larger than line 4, enter -0-. This is your taxable income.	6

Usually tax owed is looked up from a tax table.  Use the portion of a tax table shown below for the next question.

#2 Points possible: 5. Total attempts: 5

Use the table provided to determine the tax the couple owes, using the taxable income you found in the first question.

$

Alternatively, the couple could calculate the tax based on tax rate information.  A portion of the rate table from 2014 is shown. 

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
Over $148,850 but not over $226,850	$28,925 plus 28% of the excess over $148,850

 

The rates you see on the right (10%, 15%, 25%, 28%) are called marginal tax rates, but most people just call them tax brackets.

#3 Points possible: 10. Total attempts: 5

Use the tax rates above to calculate the couple's tax on the taxable income you found in the first question.

$

Does it match the tax table?

· Yes, it is identical

· It is not identical, but it's very close (within a few dollars)

· No, it is far off

 

#4 Points possible: 10. Total attempts: 5

A commonly held belief is that marginal tax rate applies to all of a person's taxable income.   

a) Does this couple owe 15% of their taxable income?  

· Yes, they pay 15% on their whole income

· No, they only pay 15% on the part of their income over $18,150

· No, they don't pay 15% on any of their income

b) If not, what percent of their taxable income are they paying? (round to 2 decimal places). This is called the effective or average tax rate.

 %  

Sometimes people have been hesitant to accept raises, worried that it will push them into a new tax bracket and they'll end up losing money.

#5 Points possible: 10. Total attempts: 5

Suppose this couple got an unexpected $1,500 bonus at the end of the year, pushing them into the 25% marginal rate tax bracket.  

a) How much total income tax will they pay, using the rate tables from above Question 3?

$

b) After paying taxes, will the couple end up with less take-home pay because the bonus pushed them into a higher tax bracket?

· They will end up with less take-home pay

· They will end up with the same take-home pay

· They will end up with about $1,200 more take-home pay

· They will end up with $1,500 more take-home pay

 

Expressions

While we can easily calculate an individual’s taxes using the tax form, it is very tedious to have to fill out the form over and over again if you have many people that all fit the same conditions.  This is a situation where an equation with variables would be helpful.

You’ve seen equations and formulas before.  For example, the area equation for a circle, A=πr2A=πr2  , is a an equation that relates two variables, r and A.  Variables are letters used to represent unknown or changeable quantities.  A formula or equation relates two or more variables, usually showing how one variable can be calculated from the other variables.

An expression consists of numbers and variables.  It does not contain an equals sign, whereas an equation always does include an equal sign.  An inequality is like an equation, but involves an inequality sign.

Examples:

3x+2y+43x+2y+4	2x2+52x2+5	Expressions
y=2x2+5y=2x2+5	3x−2y=43x-2y=4	Equations
y≤2t+3y≤2t+3	a+2b≥4a+2b≥4	Inequalities

 

In math, the steps we take depend on whether we have an expression, an equation, or an inequality.  With expressions, we often simplify, by combining like terms and distributing.  Sometimes we might evaluate an expression by replacing the variables with values and calculating the value.

· Combining like terms:  Terms can only be added only if they contain the same power of the same variables.  For example, 3x and 5x are like terms, but 2 and x2 are not.

· Distributing: a(b+c)=ab+aca(b+c)=ab+ac 

If you haven't worked with simplifying and evaluating expressions before, you may want to watch some of these videos:

· Introduction to Variables and Variable Expressions  [+]

· Introduction to the Distributive Property  [+]

· Simplifying Algebraic Expressions  [+]

· Evaluating Algebraic Expressions  [+]

#6 Points possible: 5. Total attempts: 5

Simplify this expression:   3x+4−5x+63x+4-5x+6 

   

#7 Points possible: 5. Total attempts: 5

Simplify this expression:   3(x−2)3(x-2) 

   

#8 Points possible: 5. Total attempts: 5

Simplify this expression:   5(2x−3)−4(3x+2)5(2x-3)-4(3x+2) 

   

Evaluate these expressions using the given values for the variables:

#9 Points possible: 5. Total attempts: 5

Evaluate 3x3x  if x=6x=6 

#10 Points possible: 5. Total attempts: 5

Evaluate 4x−24x-2  if x=−5x=-5 

#11 Points possible: 5. Total attempts: 5

Evaluate 3t2−5t+33t2-5t+3  if t=−2t=-2 

#12 Points possible: 5. Total attempts: 5

Evaluate LWLW  if L=5L=5  and W=4W=4 

#13 Points possible: 5. Total attempts: 5

Evaluate πr2πr2  if r=6r=6 .  Round your answer to the nearest whole number.  

Revising Taxes

While tax tables and the tax rates work well for calculating tax for a single individual, a business might want to create a spreadsheet that automatically calculates the tax for an individual based on their taxable income.  To do this, they need to write a formula. Let T be amount of tax owed, x be their taxable income, and w be their wage income.

Assume that we're only interested in couples with taxable incomes between $18,150 and $73,800.

#14 Points possible: 5. Total attempts: 5

Using the tax rate table as a guide, write an equation that will take taxable income, x, and compute the tax, T, they owe. 

   

#15 Points possible: 5. Total attempts: 5

Simplify the formula you just found using distribution and combining like terms, as needed.  (If you had already simplified the formula, just go ahead and enter that again) 

   

Building off the last set of questions, now assume also that we're only interested in couples who fill out a 1040EZ and only have wage income.

#16 Points possible: 5. Total attempts: 5

Using your previous formula and the 1040EZ form as guides, write an equation that will take their wage income, w, and compute the tax, T, they owe.  Continue to assume their taxable income is between $18,150 and $73,800.

   

#17 Points possible: 5. Total attempts: 5

Simplify the formula using distribution and combining like terms, as needed.

   

HW 2.1

#1 Points possible: 5. Total attempts: 5

Which of the following was one of the main mathematical ideas of the lesson?

· It does not matter how you write your calculations as long as you get the correct answer.

· Taxes are very complicated, and tax forms are hard to complete.

· In order of operations, you do operations in this order: 1) Within parentheses; 2) Exponents; 3) Multiplication; 4) Division; 5) Addition; 6) Subtraction.

· Part of quantitative reasoning is being able to read, interpret, and use quantitative information to perform a task.

#2 Points possible: 20. Total attempts: 5

In the lesson, you worked with the tax rate table from 2014 for couples. The table below shows the tax brackets for 2015 for single workers.

Taxable Income	Tax Rate
$0 to $9,225	10%
$9,226 to $37,450	$922.50 plus 15% of the amount over $9,225
$37,451 to $90,750	$5,156.25 plus 25% of the amount over $37,450
$90,751 to $189,300	$18,481.25 plus 28% of the amount over $90,750
$189,301 to $411,500	$46,075.25 plus 33% of the amount over $189,300
$411,501 to $413,200	$119,401.25 plus 35% of the amount over $411,500
$413,201 or more	$119,996.25 plus 39.6% of the amount over $413,200

a. What tax rate does every single worker pay on the first $9,225 of taxable income? %

b. Calculate the income tax for a single person who has $25,000 of taxable income. $

c. Calculate the income tax for a single person who has $63,500 of taxable income. $

d. Refer to your answer for part (c). The total tax in part (c) is what percentage of the person’s taxable income? Round to the nearest one percent. %

#3 Points possible: 5. Total attempts: 5

Consider the person from part (b) of the last question, who has $25,000 of taxable income. Which of the following expressions can be used to compute how much tax that person owes?

· 0.15(25,000−9,225+922.50)0.15(25,000-9,225+922.50)

· 0.15(25,000−9,225)+922.500.15(25,000-9,225)+922.50

· 0.15×25,000−9,225+922.500.15×25,000-9,225+922.50

· 0.15×25,0000.15×25,000

#4 Points possible: 5. Total attempts: 5

The expression below shows another way to calculate the person's tax who has $25,000 in taxable income:

 0.10(9,225)+0.15(25,000−9,225)0.10(9,225)+0.15(25,000-9,225) 

Based on this expression, select the statement that describes how the income is taxed.

· He pays 10% tax on his income.

· He pays 10% in tax on the first $9,225 of his income. He pays 15% on his income over $9,225.

· He pays 15% tax on his income.

#5 Points possible: 5. Total attempts: 5

Congratulations! You won a lottery prize and have a taxable income of $1,025,400. Use the table below to answer the following questions.

Taxable Income	Tax
$0−$85,500	10% of taxable income
$8,500−$34,500	$850 plus 15% of excess over $8,500
$35,500−$83,600	$4,750 plus 25% of excess over $34,500
$83,600−$174,400	$17,025 plus 28% of excess over $83,600
$174,400−$379,150	$42,449 plus 33% of excess over $174,400
$379,150 plus	$110,016.50 plus 35% of excess over $379,150

a. How much tax will you pay on your winnings? $

b. Which of the following expressions can be used to calculate the tax?

· $1,025,400 - 0.35($379,150 - $110,016.50)

· ($1,025,400 + $110,016.50) - ($37,650 × 0.35)

· $110,016.50 + 0.35($1,025,400 - $379,150)

· $1,025,400 - 0.35($1,025,400 - $379,150)

· 0.35 + $379,150($1,025,400 - $110,016.50)

#6 Points possible: 15. Total attempts: 5

Miguel is moving and wants to estimate what his electricity bill will be in his new apartment. He looks at old bills and sees that he uses around 700 kWh of electricity each month. The utility company charges $6 each month plus 6.726 cents per kWh for the first 500 kWh and 8.136 cents per kWh for any kilowatt-hours above 500.

a. How much will Miguel pay for 700 kWh of electricity? People often make a common error in situations like this. The purpose of the next two questions is to help you recognize this error and correct your work in part (a) if necessary. $

b. If someone bought three items for $1.50, 37 cents and 5 cents, how much did they spend? $

c. Which of the following is most likely the common error in part (b)?

· Making an addition error such as 37 + 5 = 45 cents

· Forgetting to change the cents to dollars: 1.50 + 37 + 5 = $43.50

· Leaving off the decimal: 1.50 + 37 + 5 = $4,350

#7 Points possible: 33. Total attempts: 5

Suppose it was determined that the water footprint for a typical American is 2,483 m3/year.

a. A family of three would like to reduce their water footprint so that it is 75% of the typical American’s water footprint. Which calculation shows how they can estimate their target water footprint for one day? There may be more than one correct answer.

· 2,500×3×0.752,500×3×0.75

· 2,500×3÷0.752,500×3÷0.75

· (3×2,500×34)÷365(3×2,500×34)÷365

· 2,500÷(365×0.75)×32,500÷(365×0.75)×3

· 2,500×3×43÷3652,500×3×43÷365

· 3×(2,500×0.75)÷3653×(2,500×0.75)÷365

· 3×2,500×0.75÷3653×2,500×0.75÷365

b. One thing a person can do to reduce his or her water footprint is to use less water every day. If each American were to reduce his or her daily water use by 2 m3 (528 gallons), how would you calculate the new annual water footprint for a typical American? There may be more than one correct answer.

· 2,483−365×22,483-365×2

· 2,483−2×3652,483-2×365

· 2,483×365−22,483×365-2

· (2,483÷365−2)×365(2,483÷365-2)×365

· 2,483÷365−22,483÷365-2

· (2,483−2)×365(2,483-2)×365

· 2,483−(2×365)2,483-(2×365)

c. Which of the following would cause the greatest decrease in the American water footprint?

· Each American decreases his or her daily water footprint by 0.3 m3.

· Each American decreases his or her daily water footprint to 95% of what it is now.

· Each American decreases his or her annual water footprint by 120 m3.

· Each American decreases his or her annual water footprint to 94% of what it is now.