SOLUTION: A researcher orders a broth of 7.5% glucose for her lab. However, she needs a stronger broth, one that is 24.9% glucose. Fortunately, she has 26.9 liters of 36.1% glucose broth in
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Question 86258: A researcher orders a broth of 7.5% glucose for her lab. However, she needs a stronger broth, one that is 24.9% glucose. Fortunately, she has 26.9 liters of 36.1% glucose broth in the stock room. How much 24.9% glucose broth can she make?
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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
