document.write( "Question 511352: In 5 years the ratio of Alvaro’s age to Alyssa’s age will be 3:5. In ten years, the ratio of Alvaro’s age to Alyssa’s age will be 2:3. What is the sum of their current ages?
\n" ); document.write( "Answer
\n" ); document.write( " a. 20
\n" ); document.write( " b. 30
\n" ); document.write( " c. 35
\n" ); document.write( " d. 40
\n" ); document.write( " e. 15 \n" ); document.write( "

Algebra.Com's Answer #342170 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"a\"$ = Alvero's age now
\n" ); document.write( "Let $\"b\"$ = Alyssa's age now
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F5+\"$
\n" ); document.write( "(2) $\"+%28+a+%2B+10+%29+%2F+%28+b+%2B+10+%29+=+2%2F3+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(1) $\"+5%2A%28+a+%2B+5+%29+=+3%2A%28+b+%2B+5+%29+\"$
\n" ); document.write( "(1) $\"+5a+%2B+25+=+3b+%2B+15+\"$
\n" ); document.write( "(1) $\"+5a+-+3b+=+-10+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+3%2A%28+a+%2B+10+%29+=+2%2A%28+b+%2B+10+%29+\"$
\n" ); document.write( "(2) $\"+3a+%2B+30+=+2b+%2B+20+\"$
\n" ); document.write( "(2) $\"+3a+-+2b+=+-10+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Multiply both sides of (1) by $\"2\"$ and
\n" ); document.write( "multiply both sides of (2) by $\"3\"$
\n" ); document.write( "Then subtract (2) from (1)
\n" ); document.write( "(1) $\"+10a+-+6b+=+-20+\"$
\n" ); document.write( "(2) $\"+-9a+%2B+6b+=+30+\"$
\n" ); document.write( " $\"+a+=+10+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+5a+-+3b+=+-10+\"$
\n" ); document.write( "(1) $\"+5%2A10+-+3b+=+-10+\"$
\n" ); document.write( "(1) $\"+-3b+=+-10+-+50+\"$
\n" ); document.write( "(1) $\"+b+=+20+\"$
\n" ); document.write( "The sum of their ages is 30
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+%28+a+%2B+5+%29+%2F+%28+b+%2B+5+%29+=+3%2F5+\"$
\n" ); document.write( "(1) $\"+%28+10+%2B+5+%29+%2F+%28+20+%2B+5+%29+=+3%2F5+\"$
\n" ); document.write( "(1) $\"+15%2F25+=+3%2F5+\"$
\n" ); document.write( "(1) $\"+3%2F5+=+3%2F5+\"$
\n" ); document.write( "OK
\n" ); document.write( "(2) $\"+%28+a+%2B+10+%29+%2F+%28+b+%2B+10+%29+=+2%2F3+\"$
\n" ); document.write( "(2) $\"+%28+10+%2B+10+%29+%2F+%28+20+%2B+10+%29+=+2%2F3+\"$
\n" ); document.write( "(2) $\"+20%2F30+=+2%2F3+\"$
\n" ); document.write( "(2) $\"+2%2F3+=+2%2F3+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );