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Mathematics fractions:

Darius, Ellen and Farhan each had some marbles. They traded marbles with one another. In the 1st round, Darius gave 1/5 of his marbles to Ellen.

In the 2nd round, Ellen gave 1/4 of his marbles to Farhan.

In the 3rd round, Farhan gave 1/2 of his marbles to Darius.

Darius had 45 marbles, Ellen had 30 marbles, and Farhan had 25 marbles left in the end.

How many marbles had each of them at first?

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Related questions

For this scenario, the manager at Shooters needs to know how advertising will effect customer turn out. In other words, how much should he spend each week in order to get the biggest return on his money. To that end, the manager at Shooters also recorded data relating how much he spent on weekly advertisements, such as fliers and commercials, with how many customers he had each week.

Week Ad $, a People, q Week Ad $, a People, q Week Ad $, a People, q
1  $          50 112 19  $           -   81 37  $       200 195
2  $       150 182 20  $       300 190 38  $       300 205
3  $       200 188 21  $       150 176 39  $       250 193
4  $       200 184 22  $          50 127 40  $       100 147
5  $       150 167 23  $       200 187 41  $          50 123
6  $           -   77 24  $       200 189 42  $       250 191
7  $       150 173 25  $       300 203 43  $          50 120
8  $           -   71 26  $       150 168 44  $           -   89
9  $       100 149 27  $       100 153 45  $       300 198
10  $       200 193 28  $       200 194 46  $       200 189
11  $       250 191 29  $       200 182 47  $           -   82
12  $       100 146 30  $       250 200 48  $           -   87
13  $       100 155 31  $          50 125 49  $           -   76
14  $       150 177 32  $       300 189 50  $       100 159
15  $          50 124 33  $       150 173 51  $          50 121
16  $       150 177 34  $       300 205 52  $          50 120
17  $       100 148 35  $       200 182      
18  $           -   76 36  $           -   80    

 

) Use this data to determine a model that describes the number of people q who come to Shooters as a quadratic function of the amount of money spent on ads.

Give a graph of the customer versus advertising data. Then state the formula that expresses how many customers he can expect based on advertising expenses, q(a).

2) Use the derivative of the quadratic function you found in question 1 to determine what amount should be spent on advertising each week in order for Shooters to achieve a maximum number of customers?  How many customers would come if the owner spent the maximum on advertising?

QUA0002 – Assignment  # 1 (10 %)
 
There are 25 questions distributed over 20 exercises; each question is worth 1 point for a total of 25,  then converted to base 10.
 Kindly answer all questions and show your work.
 
EXERCISES

  1. A hitch and trailer listed at $2149.00 has a net price of $1360.00. What is the rate of 
    discount? Give your answer in percentage rounded to nearest 100th.


  2. Rina Boutique advertises a discount of $54.72 on sandals. If the discount is 33.5%, for 
    how much were the sandals sold? Round to nearest 100th.


  3. A 14% discount on a dryer that Gell-Mann purchased, amounted to $70.00. Calculate the 
    net price. 


  4. A microscope is listed for $477.00 less 19 2/3 %, 9%, 7.7%. What is the equivalent single 
    rate of discount that was allowed? Round to nearest 100th. 


  5. Lamb Goldsmith sells watches for $840.00 less 12.55%. Its competitors across the 
    street offer the same type of watch for $860.00 less 13.25%, 11.5%. What additional rate 
    of discount (percentage) must Lamb offer to meet the competitor's price? Round to 
    nearest 100th.


  6. An invoice for $6200.00, dated May 28, 3/10, 1/20, n/60, was received on May 30. What 
    payment must be made on June 5 to reduce the debt to $4760.00? Approximate to the 
    nearest 100th. 


  7. What amount will reduce the amount due on an invoice of $9410.25 by $842.00 if the terms 
    of the invoice are 5/10, n/30 and the payment was made during the discount period?
    Approximate to nearest 100th. 


  8. On 19 June, an invoice dated 18 June for $6250.00 less 17%, 16%, terms 5/10, n/30, was 
    received by Heisenberg Distributors. What is the amount due if the invoice is paid in 
    full on 27 June? Round to nearest 100th. 


  9. The Scientific Store received an invoice for $6710.00 dated July 13, terms 5/10, 2/30, 
    n/90, for a shipment of skis. Calculate the partial payments made 20 July to reduce the 
    balance to $4000.00 Round to nearest 100th.


  10. Purcell Export received an invoice dated August 21 from Dutch Specialties of Amsterdam with 
    terms 5/20, n/45 for: 10 wood trays at $37.45 each; 35 wood planters at $43.75 each;
    50 wood bowls at $37.25 each.

    a)What is the amount due if the invoice is paid in full on September 6? Round to nearest 100th.

b)If only a partial payment is made on the last day  of the discount period, what amount is due to reduce the outstanding balance to $1500.00? Round to nearest 100th. 



  1. An invoice for $4755.00, dated 27 March, terms 3/10 E.O.M., was received 29 March. What 
    payment must be made on 10 April to reduce the debt to $1900.00? Round to nearest 100th. 


  2. Aronian Import received an invoice dated January 5 for a shipment of goods received 
    January 11. The invoice was for $5525.00 less 40%, 8% with terms 3/20 R.O.G. How much 
    must Aronian Import pay on January 20th to reduce its debt by $3000.00? 


  3. Find the cost of an item that was sold for $4230.00 in order to realize a margin of 113% 
    based on cost. Round to nearest 100th. 


  4. Karpov Dealers bought tires from a wholesaler at $75.00 dollars each and sold them 
    at a mark-up of 25% of cost.

    a)Calculate the selling price of one tire. Approximate to nearest 100th.

    b)Calculate the rate of markup based on the selling price of one tire. Approximate to nearest 100th.


  5. Hume's pet shop purchases cat litter for $15.00 less 20% per bag. The store's overhead is 45% 
    of cost and Hume requires a profit of 20 % of cost.

    a)For how much should a bag be sold?  Round to nearest 100th.

b)Calculate the amount of markup.  Approximate to nearest 100th.



  1. A bike shop reduces the price of a bike for quick sale from $455.00 to $395.00.

    a)Compute the markdown.  

    b)Compute  the markdown rate in percentage to the nearest 100th. 


  2. The regular selling price of merchandise sold in a store includes a margin of 62% based 
    on selling price. During a sale, an item which cost the store $231.25 was marked down 
    47%. For how much was the item sold? Approximate to nearest 100th. 


  3. A furniture store sold a bed regularly priced for $990.00 for $720.00. The bed was 
    originally purchased for $600.00 less 40%. The store's overhead is 25% of the regular 
    selling price. Calculate the rate of markdown (as percentage to nearest 100th) at which 
    the bed was sold. Round to nearest 100th.


  4. A furniture store sold a bed regularly priced for $990.00 for $720.00. The bed was 
    originally purchased for $600.00 less 40%. The store's overhead is 25% of the regular 
    selling price. Calculate the operating profit or loss at the sale price. Round to nearest 100th.


 
 

  1. An answering machine cost a dealer $220.00 less 31.5%, 7%. It is regularly priced at 
    $212.00. The dealer's overhead is 17% of the regular selling price and the answering 
    machine was cleared out for $175.45.

    a)What is the regular markup based on selling price? Round to nearest 100th.

    b)What was the rate of markdown at which the  answering machine was sold? Round to nearest 100th. 


Total:   /25   or    /10

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