- WELCOME TO A LESSON ON PROBLEM SOLVING.
THE GOAL OF THIS VIDEO IS TO SOLVE
A VARIETY OF PROBLEMS MATHEMATICALLY.
NOW WHEN WE START PROBLEM SOLVING,
THE FIRST STEP IS GOING TO BE TO READ THE QUESTION SEVERAL TIMES
TO UNDERSTAND EXACTLY WHAT YOU'RE LOOKING FOR,
THEN WE WILL ASSIGN NEW VARIABLES TO THE UNKNOWNS,
THEN WE WANT TO SET UP AN EQUATION AND SOLVE.
SO LET'S GO AHEAD AND TAKE A LOOK AT THIS FIRST EXAMPLE.
6 FEWER THAN 4 x A NUMBER IS 78.
FIND THE NUMBER.
SO WE HAVE TO REPRESENT 6 FEWER THAN 4 x A NUMBER.
WELL, LETS START WITH HOW WE WOULD REPRESENT THE NUMBER.
LET'S LET X = THE NUMBER WE'RE LOOKING FOR.
NEXT, WE WANT 6 FEWER THAN 4 x THIS NUMBER X.
WELL, LET'S START WITH 4 x A NUMBER.
WELL, THAT WOULD BE 4X, BUT WE WANT 6 FEWER THAN 4 x A NUMBER.
SO 6 FEWER THAN 4X WOULD BE 4X - 6 AND IS MEANS EQUALS 78.
SO HERE'S OUR EQUATION.
AGAIN, 6 FEWER THAN 4 x SOME NUMBER X.
SO NOW WE NEED TO SOLVE THIS EQUATION.
SO THE FIRST STEP, BECAUSE THERE'S NO FRACTIONS,
DECIMALS, OR PARENTHESIS, IS TO ADD OR SUBTRACT
IN ORDER TO START ISOLATING THE VARIABLE X.
SO WE'LL ADD 6 TO BOTH SIDES, WHICH WOULD GIVE US 4X = 84.
THIS IS ATTACHED BY MULTIPLICATION
SO WE'LL DIVIDE BOTH SIDES BY 4 AND WE HAVE X = 21.
AND TO CHECK THIS, 4 x 21 = 84 - 6 = 78 AND THAT CHECKS.
MOVING ALONG, THE UNITS IN SHANTA'S APARTMENT COMPLEX
ARE CONSECUTIVELY NUMBERED ON EACH FLOOR.
THE SUM OF HER NUMBER AND HER NEXT DOOR NEIGHBOR'S NUMBER
IS 443.
WHAT ARE THE TWO NUMBERS?
WELL, FIRST LETS TALK ABOUT CONSECUTIVELY NUMBERED.
THAT ESSENTIALLY MEANS THAT IF ONE OF THE DOORS IS 22
THE NEXT DOOR WOULD BE 23,
WHERE IF ONE OF THE DOORS WAS 45 THE NEXT DOOR WOULD BE 46.
SO WE NEED TO REPRESENT THIS RELATIONSHIP USING VARIABLES.
SO IF X = THE FIRST NUMBER, THEN THE PATTERN THAT WE SEE HERE
IS WE HAVE TO ADD 1 TO GET TO THE NEXT CONSECUTIVE NUMBER.
SO X + 1 = THE SECOND NUMBER.
NEXT, TO FORM OUR EQUATION IT SAYS THE SUM OF HER NUMBER
AND THE NEXT NUMBER IS 443.
WELL, SUM MEANS ADDITION SO OUR EQUATION IS GOING TO BE
THE FIRST NUMBER PLUS THE SECOND NUMBER MUST EQUAL 443.
SO THERE'S OUR EQUATION TO SOLVE.
LET'S DO THE FIRST STEP BY COMBINING OUR LIKE TERMS.
SO OUR EQUATION BECOMES
2X + 1 = 443.
LET'S TAKE THIS OVER TO THE NEXT SCREEN.
NOW WE HAVE OUR BASIC TWO STEP EQUATION
SO WE WILL SUBTRACT 1 ON BOTH SIDES, DIVIDE BY 2.
WE HAVE X = 221.
NOW, BE CAREFUL.
LET'S GO BACK AND READ THE QUESTION AGAIN.
WHAT ARE THE NUMBERS?
SO WE FOUND X OR WE FOUND THE FIRST NUMBER,
BUT THE SECOND NUMBER WAS X + 1.
SO THE NUMBERS WOULD BE 221
AND THE NEXT ONE WOULD BE X + 1 OR 222.
SO THOSE ARE THE NUMBERS WE'RE LOOKING FOR IN THIS QUESTION.
LET'S GO AHEAD AND TRY ANOTHER.
SUNSET SCENES PRINTS DIGITAL PHOTOS FOR 12 CENTS EACH
PLUS $6.29 SHIPPING AND HANDLING.
YOUR WEEKLY BUDGET FOR THE SCHOOL YEARBOOK
IS $25.00.
HOW MANY PRINTS CAN YOU HAVE MADE IF YOU HAVE $25.00?
WELL, LET'S START OFF BY LETTING X = THE NUMBER OF PRINTS.
SO THE TOTAL COST IS GOING TO EQUAL 12 CENTS FOR EVERY PRINT.
WELL THAT WOULD BE 12 CENTS x X + THE SHIPPING
AND HANDLING COST OF $6.29.
SO THE EQUATION THAT WE WANT TO SOLVE,
SINCE WE HAVE $25.00 TO SPEND,
WE WANT TO SET THIS EXPRESSION FOR COST EQUAL TO $25.00.
NOW WE COULD MULTIPLY IT BY 100 TO CLEAR THE DECIMALS,
BUT SINCE WE'RE GOING TO USE THE GRAPHING CALCULATOR
LETS GO AHEAD AND JUST DO THIS IN ITS CURRENT FORM.
FIRST STEP WE WOULD SUBTRACT 6.29.
THIS WOULD GIVE US 0.12X = 18.71.
AGAIN, YOU CAN CHECK THIS ON THE GRAPHING CALCULATOR IF YOU WISH.
LET'S TAKE THIS OVER TO THE NEXT SCREEN.
SO WE HAVE 0.12X = 18.71, SOLVE FOR X HERE WE HAVE DIVIDE.
SO WE'LL DIVIDE BY 0.12 ON BOTH SIDES.
THIS WOULD SIMPLIFY TO X EQUALS.
LET'S GO AHEAD AND GET OUR GRAPHING CALCULATOR OUT
SO WE CAN TAKE 18.71 AND DIVIDE BY 0.12.
SO WE HAVE X IS APPROXIMATELY 155.92.
REMEMBER THAT X WAS THE NUMBER OF PRINTS
AND OF COURSE, WE CANNOT ORDER A FRACTION OF A PRINT.
SO IN THIS CASE WE WOULD ROUND DOWN
AND SO OUR FINAL ANSWER WOULD BE 155 PRINTS.
LET'S GO AHEAD AND TAKE A LOOK AT ONE MORE QUESTION.
THE PERIMETER OF A STANDARD BASKETBALL COURT IS 268 FEET.
THE LENGTH IS 34 FEET LONGER THAN THE WIDTH.
SO THAT'S KEY.
WE NEED TO EXPRESS THIS RELATIONSHIP.
SO THIS IS 34 FEET LONGER THAN THIS.
SO IF YOU LET THIS EQUAL X, THIS WOULD HAVE TO BE X + 34.
AND OF COURSE, THE OPPOSITE SIDES ARE EQUAL.
NOW REMEMBER WHEN WE TALK ABOUT PERIMETER
IT'S THE DISTANCE AROUND THE OUTSIDE
AND WE'RE GIVEN THAT THE PERIMETER IS 268 FEET.
SO THE EQUATION WOULD BE THE SUM OF THESE FOUR SIDES
MUST EQUAL 268.
WELL, IF WE SUM THESE FOUR SIDES,
YOU CAN SEE THERE ARE FOUR Xs.
WE'D HAVE 4X AND WE ALSO HAVE TWO 34s.
34 + 34 WOULD BE 68, MUST EQUAL 268 FEET.
SO LET'S GO AHEAD AND SOLVE THIS.
SUBTRACT 68 ON BOTH SIDES.
THIS COMES OUT TO 200.
WE'LL DIVIDE BY 4.
AGAIN, THE MOST CHALLENGING PART IS SETTING IT UP.
WE HAVE X = 50.
NOW AGAIN, WE NEED TO MAKE SURE WE ANSWER THE QUESTION.
THE QUESTION IS FIND THE DIMENSIONS OF THE COURT.
THE WIDTH IS EQUAL TO X.
WELL, X IS 50.
SO THE DIMENSIONS WOULD BE 50 FEET BY,
AND THE LENGTH IS X + 34.
50 + 34 WOULD BE 84.
SO THE DIMENSIONS OF THE BASKETBALL COURT
WOULD BE 50 FEET BY 84 FEET.
I HOPE YOU FOUND THIS VIDEO HELPFUL.