SOLUTION: The American Kennel Club recognizes 7 categories of dogs plus one for miscellaneous breeds. In 2002 Dual Championships were awarded to 141 dogs. Dual champions are dogs that show e
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Question 121566: The American Kennel Club recognizes 7 categories of dogs plus one for miscellaneous breeds. In 2002 Dual Championships were awarded to 141 dogs. Dual champions are dogs that show excellence in both breed standard and ability to perform the function for that breed. Out of those 141 dogs, one was awarded to a dog in the toy class and 3 to dogs in the herding breeds. The remaining Dual Championships were awarded to dogs in the sporting breeds and the hound breeds. There were 93 more Dual Championships awarded to dogs in the hound breeds than the sporting breeds. (Source: American Kennel Club)
Let s = number of sporting breeds awarded Dual Championships
Let h = number of hound breeds awarded Dual Championships.
Write a system of equations that could be used to determine the number of Dual Championships awarded to sporting breeds and hound breeds.
Hint: Determine the total number of Dual Championships awarded to the sporting breeds and hound breeds and use this for one equation. The second equation will be the difference in the number awarded to the two categories.
Solve each equation for your variables and express the solution as an ordered pair.
How many sporting breeds and how many hound breeds received Dual Championships?
Among the hound breeds Dual Champions, there are 12 different breeds represented with dachshunds receiving the greatest number of Dual Championships. 75 Dual Championships were awarded to dogs other than dachshunds in this class. How many dachshunds received Dual Championships in 2002? Write a system of equations to express this problem and use mathematics to justify your answer.
Let d = number of dachshunds that received a Dual Championship in 2002
let h = number of hound breeds other than dachshunds that received a Dual Championship in 2002.
Can someone help me figure this out please? thank you!
You can put this solution on YOUR website! 141 dual champions, 1 in toy class, 3 in herding class, rest in either sporting (s) or hounds (h), so
Hounds got 93 more duals than sporting, so , or .
Add the two equations to get:
Divide by 2
, therefore
22 sporting duals and
115 hound duals
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d = dachshunds with duals
h = hounds with duals not counting dachshunds
From the previous problem we know that the total of hound breeds with duals is 115. We are given that 75 of these were awarded to other than dachshunds. Therefore
