document.write( "Question 1210591: Three brothers—Leo, Sam, and Jax—are sharing a supply of energy bars during a hike. Leo starts the trip with a backpack full of bars. He eats 3 1/2 bars. After eating them, the ratio of the bars he has left to the bars he started with is exactly 3:4. Sam then takes the remaining bars. He eats half of them plus half a bar more. Jax takes what is left. He eats half of that amount plus half a bar more. After Jax is finished, there are exactly 2 bars left in the backpack. How many energy bars did Leo start with? \n" ); document.write( "

Algebra.Com's Answer #854130 by MathTherapy(10801) $\"\"$ $\"About$

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document.write( "Three brothers—Leo, Sam, and Jax—are sharing a supply of energybars during a hike. Leo starts the trip with a backpack\r\n" );
document.write( "full of bars. He eats 3 1/2 bars. After eating them, the ratio ofthe bars he has left to the bars he started with is\r\n" );
document.write( "exactly 3:4. Sam then takes the remaining bars. He eats half ofthem plus half a bar more. Jax takes what is left. He eats\r\n" );
document.write( "half of that amount plus half a bar more. After Jax is finished,there are exactly 2 bars left in the backpack. How many\r\n" );
document.write( "energy bars did Leo start with?\r\n" );
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document.write( "METHOD 1\r\n" );
document.write( "Let the multiplicative factor be x\r\n" );
document.write( "Since the ratio of the bars he has left to the bars he started with is exactly 3:4, then the number of bars\r\n" );
document.write( "he has left is 3x, and the number of bars he started with is 4x\r\n" );
document.write( "With the number of eaten bars being , or 3.5, we get: 4x - 3x = 3.5, and x = 3.5\r\n" );
document.write( "This means that the number Leo starts with is 4(3.5) = 14. \r\n" );
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document.write( "CHECK\r\n" );
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document.write( "Original number of bars: 14\r\n" );
document.write( "Number eaten by Leo: 3.5\r\n" );
document.write( "Number remaining after Leo ate 3.5: 14 - 3.5 = 10.5\r\n" );
document.write( "Number left after Sam ate  of remainder, plus  bar:\r\n" );
document.write( "Number left after Jax ate  of NEW remainder, plus bar: \r\n" );
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document.write( "As seen above, a 2-bar end-result didn't ensue. So, itw's then decided to apply a different method.\r\n" );
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document.write( "METHOD 2\r\n" );
document.write( "Let the number of bars Leo started with, be B\r\n" );
document.write( "With  being eaten, remainder is: B - 3.5\r\n" );
document.write( "With Sam eating  of remainder, plus  bar,remainder becomes:  =  = \r\n" );
document.write( "As Jax ate  of remainder, plus  bar, then NEW remainder becomes:  =  =  = \r\n" );
document.write( "Since 2 bars are now left, we get:                                                           \r\n" );
document.write( "                                                           B - 6.5 = 8 ----Cross-multiplying \r\n" );
document.write( "   Original number of bars, or B = 8 + 6.5 = 14.5\r\n" );
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document.write( "OR\r\n" );
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document.write( "Some like to go from the end to the beginning. In other words, from the 2-bar end result to the original number of bars.\r\n" );
document.write( "This is illustrated below.\r\n" );
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document.write( "End-Number of bars: 2\r\n" );
document.write( "Number of bars before Jax ate  bar, plus  of remainder:  = (2.5)*2 = 5\r\n" );
document.write( "Number of bars before Sam ate  bar, plus  of remainder:  = (5.5)*2 = 11\r\n" );
document.write( "Number of bars before Leo ate 3.5: 11 + 3.5 = 14.5 \r\n" );
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document.write( "CHECK\r\n" );
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document.write( "Original number of bars: 14.5\r\n" );
document.write( "Number eaten by Leo: 3.5\r\n" );
document.write( "Number remaining after Leo ate 3.5: 14.5 - 3.5 = 11\r\n" );
document.write( "Number left after Sam ate  of remainder, plus  bar:\r\n" );
document.write( "Number left after Jax ate  of NEW remainder, plus bar: \r\n" );
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document.write( "VOILA!!!\r\n" );
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document.write( "There's an obvious CONTRADICTION, as one method produces an orignal amount of 14, while the other finds\r\n" );
document.write( "the count to be 14.5. As a result of this. there doesn't seem to be a SOLUTION to this problem, at all!!

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