Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 397

PRACTICE

1. The owner of an apartment complex knows he can rent all 50 apart-
   ments when the monthly rent is $400. He thinks that for each $25
   increase in the rent, he will lose two tenants. What should the rent be
   for the revenue to be $20,400?


2. A grocery store sells 4000 gallons of milk per week when the price is
   $2.80 per gallon. Customer research indicates that for each $0.10
   decrease in the price, 200 more gallons of milk will be sold. What does
   the price need to be so that weekly milk sales reach $11,475?


3. A movie theater’s concession stand sells an average of 500 buckets of
   popcorn each weekend when the price is $4 per bucket. The manager
   knows from experience that for every $0.05 decrease in the price, 20
   more buckets of popcorn will be sold each weekend. What should the
   price be so that $2450 worth of popcorn is sold? How many buckets will
   be sold at this price (these prices)?


4. An automobile repair shop performs 40 oil changes per day when the
   price is $30. Industry research indicates that the shop will lose 5 cus-
   tomers for each $2 increase in the price. What would the shop have to
   charge in order for the daily revenue from oil changes to be $1120? How
   many oil changes will the shop perform each day?


5. A fast food restaurant sells an average of 250 orders of onion rings each
   week when the price is $1.50 per order. The manager believes that for
   each $0.05 decrease in the price, 10 more orders are sold. If the man-
   ager wants $378 weekly revenue from onion ring sales, what should she
   charge for onion rings?


6. A shoe store sells a certain athletic shoe for $40 per pair. The store aver-
   ages sales of 80 pairs each week. The store owner’s past experience
   leads him to believe that for each $2 increase in the price of the shoe,
   one less pair would be sold each week. What price would result in $3648
   weekly sales?

✔SOLUTIONS

1. P = 400 + 25x Q = 50 − 2x R = (400 + 25x)(50 − 2x)
   20,400 = (400 + 25x)(50 − 2x)
   20,400 = 20,000 + 450x − 50x^2
   50 x^2 − 450x + 400 = 0

PRACTICE

1. The owner of an apartment complex knows he can rent all 50 apart-
   ments when the monthly rent is $400. He thinks that for each $25

PRACTICE

1. The owner of an apartment complex knows he can rent all 50 apart-