document.write( "Question 162620: In a local pet store , the cats sell for $10 each and the canaries sell for $15 each. the total value was $360. one night the shop owner forgot to close the cages. 2 cats and half of the canaries are gone. if the total value is now $220, how many of each were present before escape?\r
\n" ); document.write( "\n" ); document.write( "I was asked to find the solution by writing and solving a system of 2 linear equations.\r
\n" ); document.write( "\n" ); document.write( "so far i have that: k= number of cats and c= number of canaries\r
\n" ); document.write( "\n" ); document.write( "And what i think the equations might be: $\"+10k%2B15c=360+\"$
\n" ); document.write( " and $\"+20%2B1%2F2c=220+\"$ \r
\n" ); document.write( "\n" ); document.write( "Am i correct and if not how can i modify my equations to solve the equation easier? thanks.\r
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Algebra.Com's Answer #119831 by jojo14344(1513) $\"\"$ $\"About$

You can put this solution on YOUR website!
,b>
\n" ); document.write( "Good, $\"+10k%2B15c=360+\"$ -------------------------> EQN 1
\n" ); document.write( "we get, $\"k=%28360-15c%29%2F10\"$ ----------------------> EQN 2
\n" ); document.write( "But $\"cross%2820%2B1%2F2c=220%29\"$ , we'll figure it out oks,
\n" ); document.write( "2 cats are gone, so --> $\"k-2\"$ right?
\n" ); document.write( "1/2 canaries are gone, so --> $\"%281%2F2%29c\"$ right?
\n" ); document.write( "New value when they're gone, $\"220\"$
\n" ); document.write( "Putting into eqn.
\n" ); document.write( " $\"10%28k-2%29%2B15%281%2F2%29c=220\"$ ------------------------> EQN 3
\n" ); document.write( "subst, EQN 2 in EQN 3:
\n" ); document.write( " $\"10%28%28360-15c%29%2F10-2%29%2B15%281%2F2%29c=220\"$
\n" ); document.write( " $\"10%28%28360-15c-20%29%2F10%29%2B7.5c=220\"$ Get LCD
\n" ); document.write( " $\"cross%2810%29%28360-15c-20%29%2Fcross%2810%29%2B7.5c=220\"$ ,
\n" ); document.write( " $\"360-20-220=15c-7.5c\"$ , combine similar terms
\n" ); document.write( " $\"120=7.5c\"$ ---> $\"cross%28120%2916%2Fcross%287.5%29=cross%287.5%29c%2Fcross%287.5%29\"$
\n" ); document.write( " $\"c=16\"$ , TOTAL CANARIES BEFORE ESCAPING
\n" ); document.write( "For cats, go back EQN 2:
\n" ); document.write( " $\"k=%28360-15%2A16%29%2F10=%28360-240%29%2F10\"$
\n" ); document.write( " $\"k=12\"$ , TOTAL CATS BEFORE ESCAPING
\n" ); document.write( "In doubt? Go back eqn 1:
\n" ); document.write( " $\"10%2A12%2B15%2A16=360\"$
\n" ); document.write( " $\"120%2B240=360\"$
\n" ); document.write( " $\"360=360\"$
\n" ); document.write( "Go back eqn 2,
\n" ); document.write( " $\"10%2812-2%29%2B15%281%2Fcross%282%29%29%28cross%2816%298%29=220\"$
\n" ); document.write( " $\"10%2A10%2B15%2A8=220\"$
\n" ); document.write( " $\"100%2B120=220\"$
\n" ); document.write( " $\"220=220\"$
\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo
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