Question 86258

Let x=amount of 7.5% glucose broth that needs to be added to the 36.1% broth in order to get a 24.9% broth

Then 26.9+x=amount of 24.9% glucose broth that can be made.

Amount of pure glucose in the 7.5% broth is 0.075x
Amount of pure glucose in the 36.1% broth is 0.361(26.9)
Amount of pure glucose in the final broth is 0.249(26.9+x)

pure glucose before = pure glucose after

0.075x+0.361(26.9)=0.249(26.9+x)  get rid of parens

0.075x+9.7109=6.6981+0.249x  subtract 9.7109 and also 0.249x from both sides

0.075x+9.7109-9.7109-0.249x=6.6981-9.7109+0.249x-0.249x  collect like terms

-0.174x=-3.0128  divide both sides by -0.174

x=17.31 --------------------liters of 7.5% broth that's needed

26.9+17.31=44.215-------------------liters of 24.9% broth that can be made

CK

0.075(17.31)+0.361(26.9)=0.249(44.215)
1.298+9.7109=11.009
11.009=11.009



Hope this helps---ptaylor