MAT 111

   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

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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  1st faucet = 1/90 .

 

Capacity of2nd faucet = 1/75.

 

Capacity of  3rd 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 1st white square, two pennies on the 2nd white square, four on the 3rd white square, and so on for all

of the 32 white squares. Thus each white square but the 1st 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.

 

 

 

 

 

1st  white  square  has  one penny

2 nd  white square  has  2

3rd  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