- WELCOME TO A VIDEO ON THE APPLICATIONS OF INEQUALITIES.
THE GOAL OF THIS VIDEO IS TO SOLVE APPLICATION PROBLEMS.
LET'S START BY TAKING A LOOK AT KEY WORDS
AND THE TRANSLATION OF THOSE INTO INEQUALITIES.
RAOUL IS AT LEAST 8 YEARS OLD.
THE KEY WORD THERE, AT LEAST, WOULD TRANSLATE INTO X
IS GREATER THAN OR EQUAL TO 8.
AT MOST 3 STUDENTS FAILED THE COURSE.
THAT WOULD TRANSLATE INTO X LESS THAN OR EQUAL TO 3.
YOUR SPEED CANNOT EXCEED 55 MILES PER HOUR.
THAT WOULD BE X IS LESS THAN OR EQUAL TO 55.
YOUR GRADE MUST EXCEED 69 POINTS.
X MUST BE GREATER THAN 69.
LUKE IS LESS THAN 160 POUNDS.
X IS LESS THAN 160.
L.A. IS MORE THAN 300 MILES AWAY.
X IS GREATER THAN 300.
A MOVIE IS BETWEEN 105 AND 140 MINUTES
WOULD BE A COMPOUND INEQUALITY.
105 LESS THAN X LESS THAN 140.
YOU CAN ALSO READ THIS X IS GREATER THAN 105
AND X IS LESS THAN 140.
A CAR WEIGHS NO MORE THAN 1,560 POUNDS.
X IS LESS THAN OR EQUAL TO 1,560.
AND LASTLY, CARMELLA SCORED NO LESS THAN 94 POINTS
MEANING X IS GREATER THAN OR EQUAL TO 94.
OKAY, LET'S START BY TRANSLATING A SENTENCE INTO AN INEQUALITY.
THE PRICE OF SHEILA'S CAR EXCEEDED $18,500.
SO IF WE LET P = PRICE, WE KNOW IT COULD BE MORE THAN 18,500.
BUT THE REAL QUESTION IS CAN IT ALSO EQUAL 18,500?
IF WE READ THIS AGAIN, IT STATES THE PRICE EXCEEDED 18,500.
SO THAT MEANS IT COULD NOT EQUAL THAT.
IT HAD TO BE MORE THAN THAT, SO WE'RE DONE HERE.
NUMBER TWO, GLENDALE COMMUNITY COLLEGE
IS NO MORE THAN 15 MILES AWAY.
SO THE DISTANCE D IS NO MORE THAN 15 MILES AWAY.
THAT MEANS IT COULD BE LESS THAN OR EQUAL TO 15 MILES.
AND LASTLY, THE MONTHLY RENTAL CANNOT EXCEED $625,
SO IT CAN'T BE MORE THAN THIS.
SO OF COURSE IT COULD BE LESS,
BUT AGAIN, THE QUESTION BECOMES CAN IT EQUAL $625.
AND IT CAN BECAUSE $625 DOES NOT EXCEED $625.
OKAY, LET'S TAKE A LOOK AT A COUPLE PROBLEMS NOW.
PETE'S PLUMBING CHARGES $65 + $60 PER HOUR
FOR PLUMBING REPAIR.
JONAS REMEMBERS BEING BILLED LESS THAN $350.
HOW MANY HOURS WAS JONAS'S COPIER WORKED ON?
SO THE TOTAL COST WAS LESS THAN $350,
BUT THE COST IS MADE UP
OF THE $65 CHARGE + THE $60 PER HOUR CHARGE.
SO THE $65 IS OUR FIXED COST MEANING THAT DOES NOT CHANGE
BASED UPON HOW MANY HOURS IT TOOK,
BUT THE $60 PER HOUR DOES CHANGE.
SO IF WE LET X = THE NUMBER OF HOURS
WE CAN REPLACE THE COST WITH $65 + $60 PER HOUR.
SO 60 x X WHICH MUST BE LESS THAN $350.
IF WE SOLVE THIS INEQUALITY FOR X
WE'LL KNOW HOW MANY HOURS THE COPIER WAS WORKED ON.
SO WE'LL SUBTRACT 65 ON BOTH SIDES.
THIS WILL GIVE US $285.
DIVIDE BY 60.
X IS LESS THAN 4.75 HOURS.
NOW IF THIS COMPANY BILLS TO THE NEAREST HOUR,
X WOULD HAVE TO BE LESS THAN 4 HOURS.
BUT IF THEY DID BILL FOR FRACTIONS OF HOURS
IT COULD BE ANY VALUE LESS THAN 4.75 HOURS.
WE DON'T KNOW THE EXACT LENGTH OF THE JOB,
BUT THIS GIVES US AN IDEA OF WHAT IS POSSIBLE
FOR HOW LONG THE JOB TOOK.
LET'S GO AHEAD AND TAKE A LOOK AT ANOTHER.
SAMANTHA HAS TEST GRADES 86, 88, AND 78
ON HER FIRST 3 MATH TESTS.
IF SHE WANTS AN AVERAGE OF AT LEAST 80 AFTER THE FOURTH TEST,
WHAT POSSIBLE SCORES CAN SHE EARN ON THE FOURTH TEST?
WELL, REMEMBER TO FIND THE AVERAGE OF THE FOUR TESTS
WE WOULD ADD THEM UP AND DIVIDE BY 4.
SO IF WE LET X = THE SCORE OF THE FOURTH TEST,
THE AVERAGE OF THE FOUR TESTS WOULD BE OBTAINED BY TAKING X
AND ADDING IT TO THE 3 OTHER TEST SCORES
AND DIVIDING THIS BY 4.
SHE WANTS HER AVERAGE TO BE AT LEAST 80
WHICH MEANS IT HAS TO BE GREATER THAN OR EQUAL TO 80.
SO NOW IF WE SOLVE THIS FOR X,
THE FIRST THING WE DO IS MULTIPLY BOTH SIDES BY 4.
THAT WOULD GIVE US X + THIS SUM WHICH = 252
GREATER THAN OR EQUAL TO 320.
SUBTRACT 252 AND WE HAVE X HAS TO BE GREATER THAN
OR EQUAL TO 68.
SO IF THAT FOURTH TEST SCORE IS GREATER THAN OR EQUAL TO 68
SHE WILL HAVE AN AVERAGE OF AT LEAST 80
WHICH WILL GIVE HER AT LEAST A B.
OKAY, I HOPE YOU FOUND THIS VIDEO HELPFUL.
THANK YOU FOR WATCHING AND HAVE A NICE DAY.