- 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.