Algebra Demystified 2nd Ed

264 algebra De mystif ieD

EXAMPLE

How much 10% acid solution should be added to 30 liters of 25% acid

solution to achieve a 15% solution?

Let x represent the amount of 10% solution. Then the total amount of

solution is 30 + x.

10% 25% 15%

x

liters

+^30

liters

= 30 + x

liters

0.10x + 0.25(30) = 0.15(30 + x)

There are 0.10x liters of pure acid in the 10% mixture, 0.25(30) liters of pure

acid in the 25% mixture, and 0.15(x + 30) liters of pure acid in the 15%

mixture.

We solve the equation that is on the bottom row.

0100 25 30 01530

01075015 45

0

..().( )

....

.

xx

xx

+=+

+= +

− 110 010

75 00 545

45 45

3005

3

005

60

xx

x

x

x

−

=+

−−

=

=

.

...

..

.

.

==x

Add 60 liters of 10% acid solution to 30 liters of 25% acid solution to achieve

a 15% acid solution.

How much 10% acid solution and 30% acid solution should be mixed

together to yield 100 liters of a 25% acid solution?

EXAMPLE

How much 10% acid solution should be added to 30 liters of 25% acid