Question 1157584
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840 gallons batch of a tomato juice blend that contains 26% juice. The manufacturer will be combining a 6% blend and a 31% blend to achieve this. 
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26 is closer to 31 than it is to 6.  Most of the blend will be made with the 31% juice.


{{{31-6=25}}}
;
{{{31-26=5}}}
;
{{{840*(1/5)=168}}}---------gallons of the 6% tomato juice


{{{840*(4/5)=672}}}--------gallons of the 31% juice




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More generally, to make  M amount of some concentration T percent mixture, starting from H % high concentration and L % low concentration, 
let v be the amount of the H% material, and then M-v is amount of the L% material.

{{{highlight_green((Hv+L(M-v))/M=T)}}}

-

{{{Hv+LM-Lv=MT}}}

{{{Hv-Lv+LM=MT}}}

{{{(H-L)v=MT-LM}}}

{{{(H-L)v=M(T-L)}}}

{{{highlight(v=M((T-L)/(H-L)))}}}