Question 168975
Hi, Hope I can help,
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The length of the shadow of a flagpole was found to be 72 feet. The shadow of a 3 foot picket in line with the flagpole was 4 feet. what is the length of the flagpole
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This is fairly easy, to solve this we use a proportion
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The ratio( or fraction) of the length of the flagpole to its shadow is equal to the ratio ( or fraction ) of the length of the picket to its shadow
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The equation would be {{{ (length-of-flagpole)/(length-of-flagpole-shadow) = (length-of-picket)/(length-of-picket-shadow) }}}
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length of shadow of flagpole is 72 feet
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length of flagpole is unknown( so we will call it "x" feet)
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length of picket shadow is 4 feet
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length of picket is 3 feet
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Let us put the numbers in place of the words in the equation {{{ (length-of-flagpole)/(length-of-flagpole-shadow) = (length-of-picket)/(length-of-picket-shadow) }}}
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{{{ (length-of-flagpole)/(length-of-flagpole-shadow) = (length-of-picket)/(length-of-picket-shadow) }}} = {{{ (x-feet)/(72-feet) = (3 - feet)/(4-feet) }}}
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We can get rid of the "feet" in the equation
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{{{ x/72 = 3/4 }}}, now we can solve for "x", we will use cross multiplication
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{{{ x/72 = 3/4 }}} = {{{ highlight(x)/72 = 3/highlight(4) }}} = {{{ x/highlight(72) = highlight(3)/4 }}}
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{{{ (x)(4) = (72)(3) }}}, now let us multiply both sides
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{{{ 4x = 216 }}}, to find "x" we will divide each side by "4"
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{{{ 4x = 216 }}} = {{{ 4x/4 = 216/4 }}} = {{{ x = 54 }}}, you can check by replacing "x" with "54" in the equation
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{{{ x/72 = 3/4 }}} = {{{ 54/72 = 3/4 }}}, you can go further by using cross multiplication
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{{{ highlight(54)/72 = 3/highlight(4) }}} = {{{ 54/highlight(72) = highlight(3)/4 }}}
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{{{ (54)(4) = (72)(3) }}} =, multiplying both side, = {{{ 216 = 216 }}} ( True )
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"x" was the length of the flagpole, since "x" = 54, the flagpole is equal to 54 feet, don't forget to put the right unit, in this case it is feet
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Flagpole = 54 feet
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Hope I helped, Levi