document.write( "Question 529992: seven years ago B was twice as young as A,when A was3 years younger than B is now. How old is A now? \n" ); document.write( "

Algebra.Com's Answer #349843 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = A's age now
\n" ); document.write( "Let $\"b\"$ = B's age now
\n" ); document.write( " $\"+a+-+7+\"$ = A's age 7 years ago
\n" ); document.write( " $\"+b+-+7+\"$ = B's age 7 years ago
\n" ); document.write( "---------------------------
\n" ); document.write( "given:
\n" ); document.write( "7 years ago, A was 3 years younger than B is now
\n" ); document.write( "(1) $\"+a+-+7+=+b+-+3+\"$
\n" ); document.write( "7 years ago, B was twice as young as A ( half A's age )
\n" ); document.write( "(2) $\"+b+-+7+=+%281%2F2%29%2A%28a+-+7%29+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "(2) $\"+2%2A%28b+-+7%29+=+a+-+7+\"$
\n" ); document.write( "(2) $\"+2b+-+14+=+a+-+7+\"$
\n" ); document.write( "(2) $\"+a+-+2b+=+-7+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+-+7+=+b+-+3+\"$
\n" ); document.write( "(1) $\"+a+-+b+=+4+\"$
\n" ); document.write( "(1) $\"+-b+=+-a+%2B+4+\"$
\n" ); document.write( "(1) $\"+b+=+a+-+4+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+a+-2%2A%28a+-+4%29+=+-7+\"$
\n" ); document.write( "(2) $\"+a+-+2a+%2B+8+=+-7+\"$
\n" ); document.write( "(2) $\"+-a+=+-15+\"$
\n" ); document.write( "(2) $\"+a+=+15+\"$
\n" ); document.write( "A is 15
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+b+=+a+-+4+\"$
\n" ); document.write( "(1) $\"+b+=+15+-+4+\"$
\n" ); document.write( "(1) $\"+b+=+11+\"$
\n" ); document.write( "(2) $\"+b+-+7+=+%281%2F2%29%2A%28a+-+7%29+\"$
\n" ); document.write( "(2) $\"+11+-+7+=+%281%2F2%29%2A%2815+-+7%29+\"$
\n" ); document.write( "(2) $\"+4+=+%281%2F2%29%2A8+\"$
\n" ); document.write( "(2) $\"+4+=+4+\"$
\n" ); document.write( "OK \n" ); document.write( "

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