266 algebra De mystif ieD
How much water should be added to 9 liters of 45% solution to weaken it
to a 30% solution?
Think of water as a “0% mixture.”
0% 45% 30%liters+^9
liters= x + 9^
liters
0 x + 0.45(9) = 0.30(x + 9)00459030 9
0405 030270
270270xx
x+=+
+= +
−−.().()
...
..
1135030
135
030
45..
.
.
.=
=
=x
x
x
Add 4.5 liters of water to weaken 9 liters of 45% solution to a 30% solution.
How much pure acid and 30% acid solution should be mixed together to
obtain 28 quarts of 40% acid solution?
Think of pure acid as a 100% mixture. We let x represent the amount of
pure acid.
100% 30% 40%quarts+ 28 – x^
quarts=^28
quarts
1.00x + 0.30(28 – x) = 0.40(28)1000 30 28 04028
840030 112
070..().()
...
.xx
xx
x+−=
+− =
++=
−−
=
=
=840112
84084
07028
28
070
4..
..
..
.
.x
x
x
Add 4 quarts of pure acid to 28 − x = 28 − 4 = 24 quarts of 30% acid solution
to yield 28 quarts of a 40% solution.