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Anna [14]
3 years ago
5

When a number is increased by 2.8%, the result is 56. What is the original number to

Mathematics
1 answer:
Sever21 [200]3 years ago
6 0

Answer:

The original number was 54.5.

Step-by-step explanation:

If a number is increased by 2.8%, then it is 102.8% of it's original number.

In mathematics, "of" in virtually all cases means "multiplied by".

Therefore, we do the opposite:

1. Convert to a decimal.

102.8% = 1.028

2. Divide by the decimal.

56 \div 1.028 = 54.47

3. Round it to the nearest tenth.

54.47 rounds to 54.5.

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Answer:

Step-by-step explanation:

Area = 192 m²

Perimeter= 56 m

Width = x m

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2*(length + width) = 56

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(28 - x)*x = 192

28x - x*x = 192

0 = 192 - 28x + x²

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2) Equation is a quadratic equation. The roots of this equation will the dimensions of the rectangular plot.

3) The roots represent the width and length  of the rectangle.

x² - 28x +192 = 0

Sum = -28

Product =192

Factors =  -16 , -12   {-16 +(-12) = -28  & (-12)*(-16) = 192}

x² - 28x + 192 = 0

x² - 12x - 16x + (-16)*(-12) = 0

x(x  -12) - 16(x - 12) = 0

(x - 12)(x -16) =0

x -12 = 0     ; x - 16 = 0

x = 12  ; x = 16

x = 12 ,16

4) Sum of the roots = 12 + 16 = 28

Sum of the roots = half of the perimeter

5) Product of the roots = 12*16 = 192 =  area of the rectangle.

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Step-by-step explanation:

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