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?