When x is subtracted from each of 21, 22, 60 and 64, the numbers so
obtained, in this order, are in proportion. What is the mean proportional
between (x+1) and (7x+8)?
Answers
Step-by-step explanation:
Given numbers are 21,22,60 and 64
Now, x is subtracted from the number
So, (21-x) :(22-x):: (60-x):(64-x)
(22-x) (60-x) =(21-x) (64-x)
X= 8
Mean proportion of (x+1) &(7x+8)
= 24
Step-by-step explanation:
Given:-
When x is subtracted from each of 21, 22, 60 and 64, the numbers so obtained, in this order, are in proportion.
To find:-
What is the mean proportional between (x+1) and (7x+8)?
Solution:-
Given numbers are 21 ,22 ,60, 64.
If x is subtracted from the each of the numbers then they are in proportion.
(21-x) , (22-x) , (60-x) and (64-x) are in proportion.
Means = (22-x) and (60-x)
Product of means = (22-x)(60-x)
=>22(60-x)-x(60-x)
=>1320-22x-60x+x^2
=>1320 -82x +x^2
Product of means = x^2-82x +1320
Extremes = (21-x) and (64-x)
Product of extremes = (21-x)(64-x)
=>21(64-x)-x(64-x)
=>1344-21x-64x+x^2
=>1344-85x+x^2
Product of extremes = x^2 -85x +1344
We know that
In proportion ,
The product of extremes = The Product of means
=>x^2-82x +1320 = x^2 -85x +1344
On cancelling x^2 both sides then.
=>-82x +1320 = -85x +1344
=>-82x+85x = 1344-1320
=>3x = 24
=>x = 24/3
=>x = 8
The value of x = 8
Now,
x+1 = 8+1 = 9
7x+8=7(8)+8=56+8= 64
We know that
The mean Proportional of a and b is √(ab)
We have a = 9 and b = 64
Mean Proportional of 9 and 64 =
=>√(9×64)
=>√576
=>24
Answer:-
Mean Proportional of x+1) and (7x+8) is 24
Used formulae:-
1)
In proportion ,
The product of extremes = The Product of means
2)The mean Proportional of a and b is √(ab)