### Ex: Linear Equation Application (Cost of a Rental Car)

– A CAR RENTAL COMPANY

CHARGES $210 PER WEEK PLUS $.15 PER MILE

TO RENT A CAR. HOW MANY MILES CAN YOU DRIVE

IN ONE WEEK FOR $336? SO WE WANT TO START

BY FOCUSING ON THIS FIRST SENTENCE. WE WANT TO BE ABLE

TO READ THIS AND THEN MOUNT AN EQUATION

TO MODEL THE TOTAL CHARGES FOR A RENTAL CAR. SO WE’LL START BY IDENTIFYING

THE VARIABLES THAT WE’LL USE

IN OUR EQUATION. THERE’S GOING TO BE

A TOTAL COST, A WEEKLY COST

AND A MILEAGE COST. SO LET’S LET BIG C EQUAL

THE TOTAL COST IN DOLLARS. LET’S LET W EQUAL THE NUMBER

OF WEEKS AND THEN WE’LL LET M EQUAL

THE NUMBER OF MILES DRIVEN. SO NOTICE THE TOTAL COST

IS AFFECTED BY THE NUMBER OF WEEKS

THAT YOU HAVE THE CAR AS WELL AS HOW MANY MILES

YOU DRIVE. SO THE EQUATION FOR THIS

SITUATION WOULD BE BIG C THE TOTAL COST IS GOING TO BE EQUAL TO $210 x THE NUMBER

OF WEEKS SO THAT WOULD BE 210W + $.15

PER MILE, WHICH WOULD BE 0.15 x M. AND NOW USING THIS EQUATION

HERE, WE SHOULD BE ABLE TO ANSWER

THE QUESTION. WE WANT TO KNOW HOW MANY MILES

YOU CAN DRIVE IN ONE WEEK FOR $336. SO IF THE TIME IS ONE WEEK, WE

KNOW THAT W IS EQUAL TO ONE, THEN IF YOU HAVE A TOTAL

OF $336 TO SPEND, THAT WOULD BE BIG C. SO NOW WE’LL SUBSTITUTE THESE

VALUES INTO THE EQUATION AND SOLVE FOR THE UNKNOWN

WHICH WILL BE M, THE NUMBER OF MILES. SO WE WOULD HAVE

336=210 x 1 + 0.15M. OF COURSE 210 x 1 IS JUST 210 AND THAT WILL SOLVE

THIS TWO STEP EQUATION FOR M SO WE’LL SUBTRACT 210

ON BOTH SIDES. THIS WOULD BE 0,

THIS WOULD BE 126=0.15M. SO NOW WE’LL DIVIDE BOTH SIDES

BY 0.15 TO SOLVE FOR M. SO THIS WOULD BE M, AND THEN

THIS QUOTIENT WILL TELL US HOW MANY MILES YOU CAN DRIVE. SO WE’D HAVE 126

DIVIDED BY 0.15 AND THEN WE’D HAVE TO MOVE

THE DECIMAL POINTS HERE BECAUSE REMEMBER WE WANT THIS

DIVISOR TO BE A WHOLE NUMBER SO I’LL MOVE THIS TWO

TO THE RIGHT AND THE SAME HERE AND SO I’LL MOVE

THE DECIMAL POINT UP AND THEN ADD TWO ZEROS,

ONE HERE AND ONE HERE. NOW WE WANT TO DETERMINE HOW

MANY 15’S THERE ARE IN 126, THAT WOULD BE 8, 8 x 5 IS 40, CARRY THE 4, 8 x 1 + 4

THAT WOULD BE 12. DIFFERENCE HERE IS 6,

WHICH IS LESS THAN 15, SO THE 8 IS CORRECT. BRING DOWN THE NEXT DIGIT. NOW WE’RE GOING TO KNOW

HOW MANY 15’S THERE ARE IN 60, THAT WOULD BE 4,

4 x 15 IS EXACTLY 60, DIFFERENCE IS 0, BUT WE STILL

HAVE ONE MORE DIGIT TO USE. BRING THE 0 DOWN HERE

AND THERE ARE 0 15’S IN 0 SO WE PUT A 0 HERE,

0 x 15 IS 0, AND WE SUBTRACT THE DIFFERENCE

OF 0. WE’VE USED ALL THE DIGITS SO

WE KNOW THAT M IS EQUAL TO 840 WHICH MEANS YOU WOULD BE ABLE

TO DRIVE A TOTAL OF 840 MILES.

haha,, interesting but there is much much simpler way…

u know u got $336, and want to know no. of miles that can be driven in a week…

hence 336-210 = 126

now cost of one mile = .15 so 126/0.15 = 840…

Why complicate math further brother ? it is already so complicated lol..

Yes, you are correct, but part of understanding math is to be able to write equations to represent situations. This is why I went through this process. Thank you for the comment and for watching.

Thank you so much. This is the right way to understand the subject.