Algebra Demystified 2nd Ed

322 algebra De mystif ieD

The plant should produce and sell more than 50,000 CDs per month in

order to make a profit.

Mary inherited $16,000 and will deposit it into two accounts, one paying

634 % interest and the other paying 521 % interest. What is the most she can

deposit into the 512 % account so that her interest at the end of a year will

be at least $960?

Let x = amount deposited in the 512 % account

0.055x = interest earned at 521 %

16,000 – x = amount deposited in the 634 % account

0.0675(16,000 – x) = interest earned at 643 %

We want the values of x for which the total interest is $960 or more, so we

solve Interest earned at 521 % + Interest earned at 634 % ≥  960.

0.055x + 0.0675(16,000 - x) ≥ 960

0 055 0 0675 16 000 960

0 055 1080 0 0675

..(, )

..

xx

xx

+-≥

+- ≥ 9960

0 0125 1080 960

1080 1080

0 0125 120

0

-+≥

--

-≥-

.

.

.

x

x

00125

0 0125

120

0 0125

9600

≤ -

• ≤

..

x

x

Mary can invest no more than $9600 in the 512 % account in order to receive

at least $960 interest at the end of the year.

An excavating company can rent a piece of equipment for $45,000 per year.

The company could purchase the equipment for monthly costs of

$2500 plus $20 for each hour it is used. How many hours per year

must the equipment be used to justify purchasing it rather than

renting it?