# Question 9f4fd

May 3, 2016

As a blended material:

26 34/41 % of the 1:10 material
73 7/41 %  of the diluting material
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Or: add 30 more measures of the diluting material

#### Explanation:

$\textcolor{b l u e}{\text{Preamble about ratios}}$

Consider the ratio of 1:10.

This consists of 1 part of something added to 10 parts of something else. So the total amount of parts is 11.

Thus a 1:10 ratio is a concentration of 1/11xx100 = 9.09bar09%

Where the bar means repeating for ever.

And 1:40 -> 1/41xx100 ~~2.439%" "to 3 decimal places
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$\textcolor{b l u e}{\text{Solving your question}}$

You have a $1 : 10$ that you need to change to $1 : 40$

$\textcolor{b l u e}{\text{Condition 1}}$

$\textcolor{b r o w n}{\text{It does not matter that you have more volume/weight}}$

What ever you use to measure the 10 use to measure a further 30 giving you $1 : \left(10 + 30\right) \to 1 : 40$

$\textcolor{b l u e}{\text{Condition 2}}$
$\textcolor{b r o w n}{\text{You wish to blend the two so that have a specific volume/weight}}$

$\textcolor{b r o w n}{\text{Some people do not like the following method but it works very well.}}$

I use the principle of a straight line graph to plot the change in concentration as you gradually add more and more of one of the constituent. Thus able to determine the exact blend needed.

The bottom axis measures the amount of diluting constituent from none at all to nothing but the diluting constituent.

$\textcolor{b r o w n}{\text{What follows is saying: the gradient of the little bit is the same all of it!}}$
So we have:$\text{ "x-:30/451=100-:1/11" }$

$\text{ } x \times \frac{451}{30} = 100 \times \frac{11}{1}$

$\text{ } x = \frac{100 \times 11 \times 30}{451}$

x=73 7/41 %  diluting material (exact value)

The amount of the original; 1:10 mixture is:

100-73 7/41 = 26 34/41 % exact value
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Check

 26 34/41 xx1/100xx 1/11 =1/41" "color(red)("This works so ok!")#