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 #854123 by ikleyn(53742) $\"\"$ $\"About$

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\n" ); document.write( "Three brothers—Leo, Sam, and Jax—are sharing a supply of energy bars during a hike. Leo starts the trip with a backpack
\n" ); document.write( "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
\n" ); document.write( "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
\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
\n" ); document.write( "energy bars did Leo start with?
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document.write( "Let X be the number of energy bars Leo did start with (the unknown value under the problem's question).\r\n" );
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document.write( "Leo eats 3.5 bars first.\r\n" );
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document.write( "The number of bars left is x-3.5.\r\n" );
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document.write( "Write the proportion as stated in the problem\r\n" );
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document.write( "     = .\r\n" );
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document.write( "From this proportion\r\n" );
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document.write( "    4x - 14 = 3x,\r\n" );
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document.write( "    4x - 3x = 14,\r\n" );
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document.write( "       x    = 14.\r\n" );
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document.write( "So, the answer to the problem's question is 14 energy bars.\r\n" );
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document.write( "You may check that this answer satisfies the problem's conditions,\r\n" );
document.write( "Thus, all the problem's conditions are consistent and do not contradict each other.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved completely.\r
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