A chemistry teacher needs to mix a 30% salt solution with a 70% salt solution to make 20 quarts of a 40%
salt solution. How many quarts of each solution should
she mix to get the desired result?

Let +a+ = quarts of 30% solution needed

Let +b+ = quarts of 70% solution needed

(1) +a+%2B+b+=+20+

(2) +%28+.3a+%2B+.7b+%29+%2F+20+=+.4+

(2) +.3a+%2B+.7b+=+8+

(2) +3a+%2B+7b+=+80+

Multiply both sides of (1) by +3+

and subtract (1) from (2)

(2) +3a+%2B+7b+=+80+

(1) +-3a+-+3b+=+-60+

+4b+=+20+

+b+=+5+

and

(1) +a+%2B5+=+20+

(1) +a+=+15+

15 quarts of 30% solution is needed

5 quarts of 70% solution is needed

check:

(2) +%28+.3a+%2B+.7b+%29+%2F+20+=+.4+

(2) +%28+.3%2A15+%2B+.7%2A5+%29+%2F+20+=+.4+

(2) +%28+4.5+%2B+3.5+%29+%2F+20+=+.4+

(2) +8%2F20+=+.4+

(2) 8=8

Step-by-step explanation: