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zysi [14]
3 years ago
8

The value of a bike depreciates by 55% per year. Work out the current value of a bike bought 2 years ago for £1300.

Mathematics
1 answer:
nikitadnepr [17]3 years ago
7 0

Year 1: 1,300 * 55% = 715  depreciation
             1,300 - 715 = 585  book value

Year 2: 585 * 55% = 321.75 depreciation
             585 - 321.75 = 263.25 book value

Year 3: 263.25 * 55% = 144.79 depreciation
             263.25 - 144.79 = 118.46 book value

If the bike was bought 2 years ago, then its current value is $263.25. 

Currently, it is the beginning of Year 3 but depreciation is computed at the end of the year.

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Makovka662 [10]
An isosceles triangle is a type of triangle where 2 sides are equal.

Picture out 2 triangles with the same base length. 
On the first triangle, its legs are twice the length of the legs of the second triangle.

To put it into variables, let:
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     A = the length of one leg the smaller triangle
    2A = the length of one leg of the bigger triangle

Given:    Perimeter of smaller triangle = 23cm
              Perimeter of bigger triangle = 43cm

Recall the formula for solving the perimeter of a triangle:
      Perimeter = A + B + C
   
where, A, B, and C are the legs of the triangle

Since the triangle involved is an isosceles triangle, therefore, we can say that
        Perimeter = 2A + B     ,   2 legs are equal ( A=C )

Substituting the given perimeter value to the formula. 
   
23cm = 2A + B                    ⇒   equation 1  (smaller triangle)
43cm = 2(2A) + B                ⇒   equation 2  (bigger triangle)

Simplifying equation 2.
                                    43cm = 4A + B
  (rearranging)             B = 43cm - 4A        ⇒ equation 3

Substituting equation 3 to equation 1:
   (equation 1)              23cm = 2A + B
                                    23cm = 2A + (43cm - 4A)
                                    23cm = -2A + 43cm
                                    2A = 43cm - 23cm
                                    2A = 20cm  ⇒   length of the leg of the bigger triangle
                                     A = 10cm   ⇒   length of the leg of the smaller triangle

To solve for the base length, just substitute the value of A to equation 3
     (equation 3)       B = 43cm - 4A
                               B = 43cm - 4(10cm)
                               B = 3 cm

Final Answer:

• For the smaller triangle, the length of the sides are 10cm, 10cm, and 3cm
• For the bigger triangle, the length of the sides are 20cm, 20cm, and 3cm
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