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I Need More Help.how Many Stamps Did Allen Buy?

The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs. Allen bought 20 stamps at the post office in 37 cents and 20 cents denominations. If the total cost of the stamps was $7.06, how many stamps did Allen buy?

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    Perimeter of isosceles triangle = 2a + b
    where a = side with similar length
    b = base
    so here, a = 8 cm less than 4 times the length of the base
    a = 4b - 8
    put this value of a in the perimeter's equation
    Perimeter = 2a + b,

      29 = 2 (4b - 8) + b,

      :29 = 8b - 16 + b,

       :29 +16 = 9b,

       :45 = 9b,

       :b = 5.


       Now the value of a = 4b - 8,

       a = 4(5) - 8,

       a = 20 - 8,

       a = 12.
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      The key to the stamp question is that the total ends in 6. Only combinations of the 37 cent stamp can result in an answer that ends in 6, so taking the 7 from the 37 cent stamp the first two multiples of seven that end in 6 are 56 and 126
      8 x 7 = 56
      so 8 stamps @37 c = 296
      so with 12 stamps left (allen only bought 20 stamps so 20 - 8 =12)
      12 x 20 = 240
      240 + 296 = 536 (so this does not work)

      18 x 7 = 126
      so 18 x 37 c = 666c
      so with 2 stamps left
      2 x 20 = 40 c
      666c + 40 c = 706 cents which = $7.06
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