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

#### tonpole

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
$$\displaystyle 70\% \times x = 100$$

$$\displaystyle \frac{70}{100} \times x = 100$$

$$\displaystyle x = 100\times \frac{100}{70}$$

#### tonpole

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%).

#### tonpole

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

#### Wilmer

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....

tonpole

#### tonpole

Thats it, thanks! Do you mind telling what grade of math this is? Because i'd really like to know how much ive forgotten.

#### Wilmer

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.

MHF Helper