**A chemist at a university needs to mix a 25% ethanol solution with a 40%ethanol solution to obtain 120mL of a 30% ethanol solution. How much of each kind is needed?**
okay yeah, the two equations i got out of this was

.25a+.40b=120--->25a+40b=12000

a+b=120(.30)---->a+b=36

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yeah? no objections??? okay.......

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yeah so i times the bottom equation by (-25) and that cancelled out the A's so i was left with

15b=11100

so i divided that out and got B=740...

i plugged that into the original equation and got A=(-704)

(-704)mL of 25% ethanol solution and 740 mL of 40% ethanol solution...

THAT CANT BE RIGHT! A NEGATIVE AMOUNT OF SOLUTION?

can someone please please please help me figure out what i did wrong?