Algebra Demystified 2nd Ed

262 algebra De mystif ieD

2. Let x represent the amount deposited at 434 %. Then the amount depos-
   ited at^541 % is 3500 − x. The interest earned at^434 % is 0.0475x; the
   interest earned at 514 % is 0.0525(3500 − x). The sum of these two quan-
   tities is 171.75.
   0 0475 0 0525 3500 171 75
   0 0475 183 75 00

..().

xx

x

+−=

+− 5525 171 75

183 75 0 005 171 75

183 75 183 75

x

x

=

−=

−−

−

00 005 12

12

0 005

2400

x

x

x

=−

= −

−

=

$2400 was deposited in the^434 % account, and 3500 − x = 3500 − 2400 =

$1100 was deposited in the 514 % account.

3. Let x represent the amount to be loaned at 16%, so 48,000 – x repre-
   sents the amount to be loaned at 19%. The total amount of return
   should be^1812 % of 48,000 which is 0.185(48,000) = 8880.

0160 19 48 000 8880

016 9120 019 8880

9

..(, )

xx

xx

+−=

+−=

1120 003 8880

9120 9120

003 240

240

003

−=

−−

−=−

=−

−

x

x

x

xx= 8000

$8000 should be loaned at 16%, and 48,000 − x = 48,000 − 8000 =

$40,000 should be loaned at 19%.

Mixture Problems

Mixture problems involve mixing two different concentrations of a substance

to obtain some concentration in between. Often these problems are stated as

alcohol or acid solutions, but there are many more types. For example, you

might want to know how many pure peanuts should be mixed with a 40%