document.write( "Question 634952: If y varies directly as x and inversely as z, and if y=3 when x=5 and z=15, find y when x=7 and z=8 \n" ); document.write( "

Algebra.Com's Answer #400041 by jsmallt9(3758) $\"\"$ $\"About$

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\"y varies directly as x\", by itself, means:
\n" ); document.write( " $\"y+=+k%2Ax\"$
\n" ); document.write( "And \"y varies inversely as z\", by itself means:
\n" ); document.write( " $\"y+=+k%2Fz\"$
\n" ); document.write( "In both equations, the \"k\" is some constant number which is called the constant of variation.

\n" ); document.write( "\"y varies directly as x and inversely as z\", combined, means:
\n" ); document.write( " $\"y+=+k%2Ax%2Fz\"$

\n" ); document.write( "To solve your problem we will first need to find the \"k\". For this we take the fact that y = 3 when x = 5 and z = 15. Substituting these numbers in for x, y and z we get:
\n" ); document.write( " $\"3+=+k%2A5%2F15\"$
\n" ); document.write( "Now we solve for k. The fraction reduces:
\n" ); document.write( " $\"3+=+k%2F3\"$
\n" ); document.write( "Now we just multiply by 3:
\n" ); document.write( " $\"9+=+k\"$
\n" ); document.write( "So the constant of variation for our equation is 9:

\n" ); document.write( "Now that we know k, our equation is:
\n" ); document.write( " $\"y+=+9x%2Fz\"$
\n" ); document.write( "We can use this to find y when x = 7 and z = 8:
\n" ); document.write( " $\"y+=+9%287%29%2F%288%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"y+=+63%2F8\"$
\n" ); document.write( "or, if you don't like improper fractions:
\n" ); document.write( " $\"y+=+7%267%2F8\"$ \n" ); document.write( "

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