The sum of the percentages of a value & its remainder...?

May 2010
4
0
Im not sure how to describe this problem, but heres goes:

I have a starting number, lets say 100. I want to figure out what number 100 is 70% percent of, when its added to 30% of its remainder. So in this case that number would be around 130:

130 x 0.7 = 91
130 - 91 = 39
39 x .3 = 11.7
91 + 11.7 = 102.7

What is the formula to solve this?
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Last edited:

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
\(\displaystyle 70\% \times x = 100\)

\(\displaystyle \frac{70}{100} \times x = 100\)

\(\displaystyle x = 100\times \frac{100}{70} \)
 
May 2010
4
0
Thanks for the reply but that formula only address what 100 is 70% of, which an easier way of calculating is simply: 100 [FONT=&quot]÷ [/FONT]0.7. I dont know how to write this in plain english so ill describe it step by step with a modified solution:

130 x 0.7 = 91 /I've assumed here that the solution is 130, so by taking 70% of this, i have 91/

(130 x 0.3) x 0.3= 11.7 /30% of the remaining 30%/

91 + 11.7 = 102.7 /added together comes close to the original number/


What im looking for is a formula that will allow me to start with a number, like 100 in this example, and find a number that it is x% (70%) of added to y% (30%) of the remaining z% (30%).
 
May 2010
4
0
This is the closest i can get, but its still off:


100 / 0.7 = a

a x 0.09 = b /30% of 30% or 9%/

a - b = n
 
Dec 2007
3,184
558
Ottawa, Canada
Let x = the mysterious number!

.3(x - .7x) + .7x = 100
solve for x: x = 126.5822...

FORMULA:
a = .3, b = .7, n = 100

x = n / (1 - ab)

Try it:
x = 100 / (1 - .3*.7)
x = 100 / (1 - .21)
x = 100 / .79
x = 126.5822....
 
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May 2010
4
0
Thats it, thanks! Do you mind telling what grade of math this is? Because i'd really like to know how much ive forgotten.
 
Dec 2007
3,184
558
Ottawa, Canada
Thats it, thanks! Do you mind telling what grade of math this is? Because i'd really like to know how much ive forgotten.
Dunno....I'd say grade 8 or 9.