document.write( "Question 1201934: All students in Ms. Fay's Spanish class are either going on the Spain trip, the Mexico trip, or both. 1/4 of the students going to Spain are also going to Mexico, and 2/7 of the students going on the Mexico trip are also going to Spain. Which of the following could be the total number of students in Ms. Fay's Spanish class?\r
\n" ); document.write( "\n" ); document.write( "(A) 26
\n" ); document.write( "(B) 27
\n" ); document.write( "(C) 28
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\n" ); document.write( "(E) 30 \n" ); document.write( "

Algebra.Com's Answer #836519 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "All students in Ms. Fay's Spanish class are either going on the Spain trip, the Mexico trip, or both.
\n" ); document.write( "1/4 of the students going to Spain are also going to Mexico,
\n" ); document.write( "and 2/7 of the students going on the Mexico trip are also going to Spain.
\n" ); document.write( "Which of the following could be the total number of students in Ms. Fay's Spanish class?
\n" ); document.write( "(A) 26
\n" ); document.write( "(B) 27
\n" ); document.write( "(C) 28
\n" ); document.write( "(D) 29
\n" ); document.write( "(E) 30
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\r\n" );
document.write( "Let x be the number of students going to the Spain trip;\r\n" );
document.write( "    y                           going to the Mexico trip;\r\n" );
document.write( "    z                           going to both trips.\r\n" );
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document.write( "We are given\r\n" );
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document.write( "     = z,\r\n" );
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document.write( "     = z.\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "     x = 4z,\r\n" );
document.write( "    2y = 7z.\r\n" );
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document.write( "The total is  x + y - z = 4z +  - z = 3z + .\r\n" );
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document.write( "So we should check the appropriate values of z, if they can produce the values of the option's list.\r\n" );
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document.write( "For short, let's make a Table\r\n" );
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document.write( "    T   A   B   L   E\r\n" );
document.write( "  -----------------------------\r\n" );
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document.write( "    z		3z + (7/2)z\r\n" );
document.write( "		\r\n" );
document.write( "    3		19.5\r\n" );
document.write( "    4		26\r\n" );
document.write( "    5		32.5\r\n" );
document.write( "    6		39\r\n" );
document.write( "    7		45.5\r\n" );
document.write( "    8		52\r\n" );
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document.write( "Looking in this Table, we see only ONE opportunity for possible solution: 26 students.\r\n" );
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document.write( "ANSWER.  Under given conditions, the only possible solution is 26 students in the class.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete explanations.\r
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\n" ); document.write( "\n" ); document.write( "Nice problem, fresh and well posed.\r
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\n" ); document.write( "\n" ); document.write( "My congratulations ( ! )\r
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