A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 305 mL of the first solution and 580 mL of the second gives a mixture that is 10.24% acid, whereas blending 85 mL of the first mixed with 490mL of the second gives a 6.10% acid mixture. What are the concentrations of sulfuric acid in the original containers?

Question

Mathematics

Joey Bridges

Today, 19:07

A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 305 mL of the first solution and 580 mL of the second gives a mixture that is 10.24% acid, whereas blending 85 mL of the first mixed with 490mL of the second gives a 6.10% acid mixture. What are the concentrations of sulfuric acid in the original containers?

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Jacquelyn Cross · Answer 1

A is the concentration of the first container, B the second container.

300a+600b=900· (15) = 13500

1.3a+6b=135

100a+500b=600· (12.5) = 7500

2. a+5b=75

Multiply eq. 2 by (-3) and add to eq. 1 to eliminate A.

3a+6b-3a-15b=135-225

-9b=-90

b=10

Then from eq. 2,

a+50=75

a=25

The first container is a 25% solution and the second container is a 10% solution