if x is subtract from each of 23 39 32 and 56 the no. so obtained in this order are in proportion what is the mean proportional between (x+4) and (3x+1)
Answers
Answer:
the answer is 3x 4x 5x 6x 7x 8x 9x
The mean proportional between (x + 4) and (3x + 1) is 12.
• Given numbers are :
23, 39, 32, and 56
If x is subtracted from of these numbers, then the numbers become (23 - x), (39 - x), (32 - x), and (56 - x) respectively.
• The numbers are said to be in proportion.
=> (23 - x) / (39 - x) = (32 - x) / (56 - x)
=> (23 - x) × (56 - x) = (32 - x) × (39 - x)
=> 1288 - 23x - 56x + x² = 1248 - 32x - 39x + x²
=> 1288 - 79x + x² = 1248 - 71x + x²
=> 1288 - 1248 = -71x + 79x + x² - x² => 40 = 8x
=> 8x = 40
=> x = 40 / 8
=> x = 5
• Therefore, the numbers (x + 4) and (3x + 1) are :
(x + 4) = 5 + 4 = 9
(3x + 1) = (3 × 5) + 1 = 15 + 1 = 16
• The mean proportional between 9 and 16 is given by:
9 : y = y : 16
=> 9/y = y/16
=> y² = 16 × 9
=> y² = 144
=> y = √144
=> y = 12
Therefore, the mean proportional is 12.