Download Notes 1.6 – Mathematical Modeling Date: _____ Algebra M

Notes 1.6 – Mathematical Modeling
Algebra M-1
Date: _____
Goal:
Vocabulary:
 Modeling

The Plan -
Examples:
1) You and your friends went to a music store to buy CDs on sale for $6 each. Together you
spent $77.76, which included a tax of $5.76. How many CD’s did you buy?
VERBAL
ALGEBRAIC
SOLVE
ANSWER
Practice:
2) You and some friends are at a restaurant. You order several $2 plates of wontons, egg rolls,
and dumplings. Your bill is $25.20, which includes tax of $1.20. Use modeling to find how
many plates you ordered.
VERBAL
ALGEBRAIC
SOLVE
ANSWER
Example:
3) A football field is about 53 yards wide and 120 yards long. A soccer field has the same area,
but is 60 yards wide. How long is the soccer field?
DIAGRAM
VERBAL
ALGEBRAIC
SOLVE
ANSWER
Practice:
4) The Malloys’ have a vegetable garden that is 8 meters long and 6 meters wide. Their
neighbors, the Smiths made a garden with the same area. However, they only had space to make
their garden 4 meters wide. Use modeling to find the length of the Smith garden.
DIAGRAM
VERBAL
ALGEBRAIC
SOLVE
ANSWER
Example:
5) A pilot is flying from LA to Chicago at a speed of 500 mph. When the plane is 600 miles
from Chicago, an air traffic controller tells the pilot that it will be 2 hours before the plane can
get clearance to land.
At what speed would the jet have to fly to arrive in Chicago in 2 hours?
VERBAL
ALGEBRAIC
SOLVE
ANSWER
The pilot knows that at her present altitude, the speed of the jet must be greater than 322 miles
per hour or the plane could stall. Is it reasonable for the pilot to fly directly to Chicago at the
reduced speed from part (a) or should the pilot take some other action.
VERBAL
ALGEBRAIC
SOLVE
ANSWER
Practice:
6) A salesperson drives at a speed of 50 miles per hour. When he is 165 miles from his
destination, he remembers he has a meeting in 3 hours. At his current speed, will he be on time
for his meeting?
VERBAL
ALGEBRAIC
SOLVE
ANSWER
7)
At what minimum speed should he travel from this point on if he wants to be on time for
the meeting?
VERBAL
ALGEBRAIC
SOLVE
ANSWER
HW: Worksheet 1.6