document.write( "Question 105347: A rancher bought 20 times as many cows as bulls. Each cow costs $1,000 and each bull costs $2,000. If the rancher spent $220,000 for this transaction, how many cows and how many bulls did the rancher buy? \n" ); document.write( "

Algebra.Com's Answer #76722 by Earlsdon(6294) $\"\"$ $\"About$

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You can start by assigning variables (letters) to the unknown quantities.
\n" ); document.write( "Let C = the number of cows and B = the number of bulls.
\n" ); document.write( "From the story, you can write:
\n" ); document.write( "C = 20B \"...bought 20 times as many cows as bulls.\"
\n" ); document.write( "The cost of each cow is $1,000 and this can be represented as ($1,000)*C
\n" ); document.write( "The cost of each bull is $2,000 and this can be represented as ($2,000)*B
\n" ); document.write( "The total cost (sum) of these two purchases is $220,000
\n" ); document.write( "Now we can write the equation to solve the problem:
\n" ); document.write( "($1,000)C + ($2,000)B = $220,000 but we can replace the C here with its equivalent C = 20B toget:
\n" ); document.write( "($1,000)(20B) + ($2,000)B = $220,000 Simplify and solve for B
\n" ); document.write( "($20,000)B + ($2,000)B = $220,000 Combine like-terms.
\n" ); document.write( "($22,000)B = $220,000 Divide both sides by $22,000 to get:
\n" ); document.write( "B = 10 The rancher bought 10 bulls.
\n" ); document.write( "C = 20B
\n" ); document.write( "C = 20(10)
\n" ); document.write( "C = 200 The rancher bought 200 cows.
\n" ); document.write( "Check:
\n" ); document.write( "($1,000)(200) + ($2,000)(10) = $200,000 + $20,000 = $220,000 \n" ); document.write( "

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