SOLUTION: What number should be added to the numbers in the ratio 5:6 so that the ratio becomes 8:9 and the sum of the terms would become 51.

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Question 779640: What number should be added to the numbers in the ratio 5:6 so that the ratio becomes 8:9 and the sum of the terms would become 51.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
What number should be added to the numbers in the ratio 5:6 so that the ratio becomes 8:9 and the sum of the terms would become 51.
:
let x = the multiplier
then
5x = one number
6x = another number
let n = the number to be added
:
"the sum of the terms become 51"
(5x+n) + (6x+n) = 51
11x + 2n = 51
:
%285x%2Bn%29%2F%286x%2Bn%29 = 8%2F9
cross multiply
8(6x+n) = 9(5x+n)
48x + 8n = 45x + 9n
48x - 45x + 8n - 9n = 0
3x - n = 0
n = 3x
replace n with 3x in the 1st simplified equation
11x + 2(3x) = 51
11x + 6x = 51
17x = 51
x = 51/17
x = 3 is the multiplier
then
n = 3(3)
n = 9 is the number to be added to satisfy the requirements
:
I'll let you check this in the original statements.