MAT 111-03 **Test 1(take-home) **Handed out Friday, September 20

**Due ** by Thursday, September 26, noon (12:00 pm)

**Late papers will be penalized:**

**–10% if I receive your paper after 12:00pm but before 4:00pm Thursday, September 26**

**–25% if I receive your paper after 4:00pm Thursday, but before 9:00am Friday, September 27**

**–50% if I receive your paper after 9:00am Friday, but before 3:00pm Friday, September 27**

**–100% if I receive your paper after 3:00pm Friday, September 27**

************************************************************************************

**Instructions**

- Enter only the
**neat**, final version of your *work*, **together with your answers**, on the spaces provided

on these sheets. ALL OF YOUR WORK AND YOUR ANSWERS SHOULD BE ON THESE

SHEETS I AM PROVIDING.

- Enter your answers in the boxes provided.

- You must show supporting work for full credit.

- Although you may consult others while working on these problems, the final work you submit

*must* be written by you.

By signing below, I am acknowledging that I have read the above Instructions, and agree to abide by them. I understand that failure to follow any of these Instructions may result in a lowering of my test score.

Your name:

Your Signature: _____________________________

**Let A, B, C, and D be the last four digits of your 8-digit student number, written in decreasing order (from the largest to the smallest). (So if your student number is 111-23-546, then for your test**

** A = 6, B = 5, C = 4 and D = 3. If your student number is 101-24-003, then A= 4, B=3, C=0, and D=0.)**

101-43-030

** **

**Write your numbers here: A = __4__ , B = __3__ , C = __1___, D = __0___**

** **

**Warning. You must use your student number. **

** **

**1**. A store has shoes that have their sale price marked down by 20%. A week later their sale price is reduced by

10%. The following week the shoes have their sale price reduced by 50%.

If the final price (before tax) of the shoes is $**AB.CD (that is, Ax$10 + Bx$1 + ** **Cx10¢ + Dx1¢),** then

what was their price before the first discount?

Let the price of shoes be $x

Now sale price = .80 *x .

After one week its price = .80*x * .90 = .72 x.

Now the following week price = .72 * 50% = .36 *x .

Now the

Final price = $AB.CD

So value of x = 100/36 * $AB.CD = $ 25/9 *AB.CD

** **

For problems 2. and 3., **r %= ** **A.BCD **% for your **A**, **B**, **C, and D** . (So, for example, if **A** = 6, **B** = 3,

**C** = 3, and **D** = 1, then **r %** = 6**.**331%).

** **

** **

** **** 2.** (a) If $1500 is invested at an annual simple interest rate of **r %**,then how much will it grow to

in 64 months? Write your answer in dollars+cents, rounded to the nearest cent.

SI = P * R /100 * T

64 months = 5 years 4 month = 16/3 year

So, interest = 16/3*1500*r/100 = $ 80 *r .

For example r= 5.431 %

So interest = $434 and 43 cents

$434 and 43 cents

(b) If $1500 is invested at an annual interest rate of **r % ** compounded monthly, how much will it

grow to in 64 months? Write your answer in dollars+cents, rounded to the nearest cent.

** **

**Amount = P * (1+ r/12)^12**

**= 1500 * (1+ 5.431/12)^12**

**= $ 2002.64**

** **

** **

**So, compound interest = 2002.64- 1500 = $502 and 64 cents**

** **

** **

** **

** **

** **

** **

** $****502 and 64 cents**

** **

**3**. How many pennies would you have if together they weigh ** r%** of a ton? Round your answer to the nearest whole

number of pennies.

a ton = 1000 Kg

let r = 6.250 %

so , I would have = 6.250 /100 * 100 kg

assuming each penny is 2.5 gm

so number of penny = 6.250 /100 * 100 * 1000 / 2.5 = 6.250 / 2.5 * 1000 = 2.5*1000 = 25000 pennies

25000 pennies

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

** **

** ****4.** There are three faucets available to fill a wading pool. The first alone would take 90 minutes to fill

the pool. The second alone would take 75 minutes to fill the pool. The third alone would take 1 hour

to fill the pool. How long would it take to fill the pool if all three faucets are used at the same time?

Write your answer in minutes+seconds, rounded to the nearest second

Capacity of 1^{st} faucet = 1/90 .

Capacity of2nd faucet = 1/75.

Capacity of 3^{rd} faucet = 1/60.

If they are used at same time so total capacity = 1/60 +1/75 + 1/90 = 37/900

So, the time taken to fill the pool = 1 / (37/900)= 900/37 = 24 minutes and 19 seconds

.

24 minutes and 19 seconds

**5**. A chessboard, like a checkerboard, has 64 squares, usually 32 white and 32 black. Imagine putting a penny

on the 1^{st} **white square**, two pennies on the 2^{nd} **white square**, four on the 3^{rd}** white square**, and so on for all

of the 32 **white squares**. Thus each **white square** but the 1^{st} contains twice as many pennies as the previous

**white square**. Assuming each penny weighs 2.5 grams, then how heavy a stack could be made from all

of the pennies? Round your answer to the nearest ton. Write your answer in tons+pounds, rounded to the

nearest pound.

1^{st} white square has one penny

2 nd white square has 2

3^{rd} white square has 4

So , n white square has 2^(n-1).pennies

So for 32 squares the number of pennies will be = ∑ 2^(n-1) for n = 1 to 32.

= 4294967295 pennies can be kept .

Now ,

Total weight = 4294967295 *2.5 gm

Now 1 ton = 1000 * 1000 gm

So weight = 4294967295 *2.5 / 10^6= 10737.42 ton.

= 10737 and 840 pounds.

10737 and 840 pounds

**For Problem 6, use I % = r % + 10 % as your annual interest rate, where r % = A.BCD % **

** is the same interest rate you used in Problems 1 and 2.**

** **

** **

**6. The following table shows all transactions on a particular credit card during the month of**

** November.**

Assume an annual interest rate of **I %**, and assume a balance of $1916.02 at the start of

November. (Thus a payment of $1916.02 at the start of November would reduce the debt to $0.)

** **

** Date** |
** Transaction** |

Nov 3 |
$2.07 video rental charged to card |

Nov 10 |
$56.18 payment for cell phone bill paid for with the credit card |

Nov 12 |
$300 payment to credit card |

Nov 21 |
$35.59 pants which were charged to card in August are returned to
Walmart, and the money is credited to the card |

Nov 30 |
$ 74.26 groceries charged to card |

Using the **average daily balance method**, calculate the interest (finance charge) for November, and

the balance due at the start of December. Write your answer in dollars+cents, rounded to the nearest cent.

I % = 10 + 5.431 = 15.431 %

At start of November = $1902.

Amount paid with credit card = 2.07 + 56.18 + 74.26 = $ 132.51

** November interest**

** **

** **

** Balance due at the start of December**