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- THE HEIGHT OF A BOOKSHELF IS 4 INCHES LESS THAN 2 x THE WIDTH.
FIND THE WIDTH AND THE HEIGHT IF THE CARPENTER EXPECTS TO USE
12 FEET OF LUMBER TO MAKE THE BOOKSHELF.
SO HERE'S OUR BOOKSHELF.
THE FIRST THING WE SHOULD RECOGNIZE IS THAT
THE HEIGHT WOULD BE THIS LENGTH HERE AND HERE.
THEN THE WIDTH WOULD BE THE LENGTH
OF THESE FOUR SHELVES, 1, 2, 3, 4.
WE DON'T KNOW THE WIDTH OR THE HEIGHT,
BUT WE KNOW THAT THE HEIGHT IS 4 INCHES LESS THAN 2 x THE WIDTH.
LET'S LET THE WIDTH BE X INCHES.
SO THIS WOULD BE X INCHES,
THIS WOULD BE X INCHES AND SO WOULD THESE TWO.
THEN THE HEIGHT IS GOING TO BE 4 INCHES LESS THAN 2 x THE WIDTH.
WELL, 2 x THE WIDTH WOULD BE 2X
AND THEN FOUR INCHES LESS WOULD BE 2X - 4.
SO THIS GREEN LENGTH OR THE HEIGHT WOULD BE 2X - 4.
AND OF COURSE, OVER HERE WE'D HAVE THE SAME.
NOW KEEP IN MIND, ALL OF THESE DIMENSIONS ARE IN INCHES.
THAT'S IMPORTANT BECAUSE THE LAST PART
IS THE CARPENTER EXPECTS TO USE 12 FEET OF LUMBER
TO MAKE THIS BOOKSHELF.
SO THIS IS IN FEET, BUT ALL THESE DIMENSIONS ARE IN INCHES,
SO WE WANT TO CONVERT 12 FEET TO INCHES.
WELL, THERE'S 12 INCHES IN 1 FOOT,
SO 12 FEET = 144 INCHES.
NOW, WE HAVE ALL THE INFORMATION WE NEED TO WRITE AN EQUATION
TO DETERMINE THE WIDTH AND THE HEIGHT OF THIS BOOKSHELF.
IF WE ADD ALL OF THESE LENGTHS UP, IT MUST EQUAL 144 INCHES.
SO WE HAVE 4Xs OR 4 x X + WE HAVE 2 LENGTHS THAT ARE 2X - 4,
SO ALL THIS MUST HAVE A SUM OF 144 INCHES.
SO NOW, WE'LL CLEAR THE PARENTHESES AND SOLVE FOR X
WHICH WILL BE OUR WIDTH.
SO WE'LL DISTRIBUTE, WELL, THIS WOULD BE 4X + 4X - 8 = 144,
COMBINE LIKE TERMS, 4X + 4X IS 8X.
SO NOW, WE'D ADD 8 TO BOTH SIDES OF THE EQUATION,
SO WE'D HAVE 8X EQUALS, THIS WOULD BE 152,
NOW DIVIDE BY SIDES BY 8,
SO WE HAVE X EQUALS THIS QUOTIENT HERE
AND 152 DIVIDED BY 8 = 19
WHICH MEANS THE WIDTH OF THE BOOKCASE IS 19 INCHES.
AND THE HEIGHT WHICH IS 2X - 4 OR 2 x 19 - 4,
THAT'D BE 38 - 4 OR 34 INCHES FOR THE HEIGHT.
NOW, LET'S GO AHEAD AND VERIFY THIS ON THE CALCULATOR.
IF WE HAVE 4 WIDTHS AT 19 INCHES AND 2 HEIGHTS AT 34 INCHES,
THIS SHOULD EQUAL 144 INCHES, AND IT DOES.
SO OUR SOLUTION IS CORRECT.
HOPE YOU FOUND THIS HELPFUL.