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What is the Number ? (Posted on 2003-03-14) Difficulty: 1 of 5
Which is the number that, multiplied by 3, then increased by three-fourths of the product, divided by 7, diminished by one-third of the quotient, multiplied by itself, diminished by 52, the square root found, addition of 8, division by 10, gives the number 2 ?

See The Solution Submitted by Ravi Raja    
Rating: 2.6250 (8 votes)

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Solution Algebraically speaking ..... | Comment 5 of 12 |
Let x = number.

Mult. by 3 : 3x

Increased by 3/4(3x) : 3x + (9/4)x = (21/4)x

Divided by 7: (21/4)x * (1/7) = (3/4)x

Dim. by 1/3 of quot. : (3/4)x - (1/3)(3/4)x = (1/2)x

Mult. by itself: (1/2)x * (1/2)x = (1/4)x^2

Dimin. by 52 : (1/4)x^2 - 52

Square root: SQRT[(1/4)x^2 - 52]

Increased by 8: SQRT[(1/4)x^2 - 52] + 8

Divided by 10: {SQRT[(1/4)x^2 - 52] +8 }/10

So, we have {SQRT[(1/4)x^2 - 52] +8 }
------------------------- = 2
10


Hence, {SQRT[(1/4)x^2 - 52] = 12

and squaring both sides gives:

(1/4)x^2 - 52 = 144 ..>

(1/4)x^2 = 196 ..>

x^2 = 784 ..>

x = 28 or x = -28
  Posted by mathemagician on 2003-07-04 04:56:10
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