January 15, 2018

Civil Rights leader and Nobel Prize winner Martin Luther King, Jr. was born January 15, 1929.  On January 13, 1979 a 15-cent stamp was issued by the United States Postal Service as part of the Black Heritage Series of commemorative stamps. In 1979 it cost 15 cents to mail a first-class letter weighing up to 1 ounce, and the current cost to mail a first-class letter weighing no more than 1 ounce is 49 cents.  Suppose $24,965,250 worth of the Black Heritage King stamps have been issued by the USPS.

 

Using only those 15-cent commemorative King stamps that have been issued, how many first-class letters weighing up to 1 ounce each could be mailed today? Express your answer to the nearest whole number.

We are told that it currently costs 49 cents to mail a first-class letter (weighing up to 1 ounce).  Since we are only to use the commemorative King stamps that have been issued, which are valued at 15 cents each, we must use 4 stamps per letter to have sufficient postage.  Therefore, each letter will contain 4 × 15¢ = 60¢ worth of postage. To determine how many letters we can mail using three King stamps per letter we need to divide the value of the total number of issued commemorative stamps by 60¢. That means $24,965,250 ÷ 0.60 41,608,750 letters can be mailed.

 

What is the total amount of money that would be saved by using a combination of commemorative 15-cent King stamps and 1-cent stamps to mail the same number of first class letters from the previous problem.

Using a combination of 15-cent King stamps and 1-cent stamps allows us to use exactly 49¢ to mail each letter since 3(15¢) + 4(1¢) = 49¢.  Therefore, it would cost 41,608,750 × 0.49 = $20,388,287.50 to mail the same number of letters as in the previous problem using 49 cents worth of postage per letter.  The total amount saved would be $24,965,250 – $20,388,287.50 = $4,576,962.50.

Another way to look at the problem is to consider that there was 11¢ lost on each of the 41,608,750 letters mailed for a total of 41,608,750 (0.11) = $4,576,962.50.

 

What is the percent decrease in the total number of letters that can be mailed using $24,965,250 worth of first class postage today compared to 1979 when the commemorative King stamp was first issued? Express your answer to the nearest tenth.

We are told that when the commemorative King stamp was first issued in 1979 the cost to mail a first-class letter was 15¢, thus, it would take one 15-cent King stamp to mail a letter.  Therefore, the $24,965,250 worth of commemorative stamps issued would mail a total of $24,965,250 ÷ 0.15 = 166,435,000 letters.  It costs 49¢ to mail a first-class letter today, so that same $24,965,250 would be enough to mail $24,965,250 ÷ 0.49 = 50,949,489.80 ≈ 50,949,489 letters. The difference in the total number of letters is 166,435,000 – 50,949,489 = 115,485,511.  The percent decrease is, therefore, 115,485,511 ÷ 166,435,000 = 0.69387756 ≈ 69.4%.

 

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Page 2
contains ONLY PROBLEMS.