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Lemur [1.5K]
3 years ago
10

if five times a number added to 4 is divided by the number plus 6 the result is nine halves, Find The Number

Mathematics
1 answer:
Leto [7]3 years ago
7 0

Answer:

8/13

Step-by-step explanation:

Let the number be x

if five times a number added to 4 is divided by the number plus 6 the result is nine halves

  • five times the number = 5x
  • five times a number added to 4 = 5x+4
  • five times a number added to 4 is divided by the number = (5x+4)/x
  • five times a number added to 4 is divided by the number plus 6 = (5x+4)/x  + 6
  • nive halves = 9*(1/2)

five times a number added to 4 is divided by the number plus 6 the result is nine halves

(5x+4)/x  + 6 = 9(1/2)

=>(5x+4)/x  + 6 -6 = 9(1/2) -6 = 9/2-6 = (9-6*2)/2 = -3/2

=>(5x+4)= -3/2 *x= -3x/2

=>2(5x+4) = -3x

=> 10x +8 = -3x

=> 10x+3x = 8

=> 13x = 8

=> x = 8/13

Thus, the number is 8/13

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Step-by-step explanation:

The formula of the nth term of the arithmetic progression is a_{n} = a + (n - 1)d

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∵ 32 = a + (n - 1)3

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→ Add 3 to both sides

∴ 35 = a + 3n

→ Switch the two sides

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→ Subtract 3n from both sides

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∴ 370 = 2an + 3n² - 3n

→ Substitute a by equation (1)

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→ Add the like terms in the right side

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→ Add 3n² to both sides

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→ Subtract 67 from both sides

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∴ n = 10 and n = 37/3

∵ n must be a positive integer ⇒ 37/3 neglecting

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