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?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! You can start by assigning variables (letters) to the unknown quantities.
Let C = the number of cows and B = the number of bulls.
From the story, you can write:
C = 20B "...bought 20 times as many cows as bulls."
The cost of each cow is $1,000 and this can be represented as ($1,000)*C
The cost of each bull is $2,000 and this can be represented as ($2,000)*B
The total cost (sum) of these two purchases is $220,000
Now we can write the equation to solve the problem:
($1,000)C + ($2,000)B = $220,000 but we can replace the C here with its equivalent C = 20B toget:
($1,000)(20B) + ($2,000)B = $220,000 Simplify and solve for B
($20,000)B + ($2,000)B = $220,000 Combine like-terms.
($22,000)B = $220,000 Divide both sides by $22,000 to get:
B = 10 The rancher bought 10 bulls.
C = 20B
C = 20(10)
C = 200 The rancher bought 200 cows.
Check:
($1,000)(200) + ($2,000)(10) = $200,000 + $20,000 = $220,000
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