# MATH HELP

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In what proportion should 95% alcohol be mixed with 30% alcohol to make 70% alcohol?

• MATH HELP -

0.......30%......70%......95%......100
.............40.......25..............

Look at the proportions above,
between 70% and 30%, the difference is 40%
and between 95% and 70%, the difference is 25%.

They should be mixed in the inverse ratio, i.e.
25 parts of 30% to 40 parts of 95%.
Converted to ratios,
25/(25+40)=25/65=5/13
40/(25+40)=40/65=9/13
So we mix (5/13) parts of 30% with (8/13) parts of 95% alcohol.

You can also solve it with algebra:
Let x be the fraction of 30% alcohol, then
30%*x+95%*(1-x) = 70%
Solve for x to get 5/13

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