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
- 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.
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- 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.
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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.)
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 .
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
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
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 .
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
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.)
| 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
Balance due at the start of December