word problem

Question

A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 330 mL of the first solution and 590 mL of the second gives a mixture that is 15.46% acid, whereas blending 85 mL of the first mixed with 495 mL of the second gives a 11.64% acid mixture. What are the concentrations of sulfuric acid in the original containers? (Round your answer to the nearest whole number.)

 

first solution ___%
second solution __%

Answer 1

x=first solution percent

y=second solution percent

330(x%)+590(y%)=15.46%(920)  (330+590=920)

85(x%)+495(y%)=11.64%(580)    (85+495)=580)

330(x%)+590(y%)=0.1546(920)

85(x%)+495(y%)=0.1164(580)

330x+590y=142.232

85x+495y=67.512

multiply the first equation by 17 and multiply the second equation by 66

5610x+10,030y=2417.944

5610x+32,670y=4455.792

subtract the first equation from the second equation

22,640y=2037.848

y=2037.848/22,640

y=0.090011

y=9% (second solution)

85x+495(9%)=67.512

85x+44.55=67.512

85x=67.512-44.55

85x=22.962

x=22.962/85

x=0.2701412

x=27% (first solution)

check:330*27%+590*9%=89.1+53.1=142.2

15.46%*920=142.232

 

85*27%+495*9%=22.95+44.55=67.5

11.64%*580=67.512

 

Answer 2

let the firs solution be x and second solution is y

 

According to the given data

 

330x+590y=1546

85x+495y=1164

 

solve x and y to get the answer