buck said "gee whiz, there must be between 10 and 20 animals in the yard!"
"yes" said chuck. "there is one more cat than there are dogs, and there is one more squirrelthan there are cats." What are the greatest possible number of dogs in the yard?? explain.
There would be 5 dogs 6 cats and 7 squirrels. Add them together there is 18. And if you go any higher then there would be 21. So the greatest amount of dogs would be 5.
omg thank you soo much!!!
No problem. Just here to help. Lol
x + y = 5
3x - y = 7
To determine the greatest possible number of dogs in the yard, we need to consider the information provided in the conversation between Buck and Chuck.
According to Buck, there must be between 10 and 20 animals in the yard. This means our answer should fall within this range.
Chuck added that there is one more cat than there are dogs. Let's represent the number of dogs as "d" and the number of cats as "c." Therefore, the number of cats would be equal to "d + 1."
Chuck also mentioned that there is one more squirrel than there are cats. Let's represent the number of squirrels as "s." Therefore, the number of squirrels would be equal to "c + 1" or "(d + 1) + 1."
To find the maximum number of dogs, we need to find an upper limit within the range of 10 to 20 that satisfies these conditions. Let's substitute the expressions we derived into the initial range:
10 ≤ d + (d + 1) + ((d + 1) + 1) ≤ 20
Now we can simplify the inequality:
10 ≤ d + d + 1 + d + 1 + 1 ≤ 20
10 ≤ 3d + 3 ≤ 20
Next, subtract 3 from each side of the inequality:
7 ≤ 3d ≤ 17
Finally, divide each side by 3 to solve for "d":
7/3 ≤ d ≤ 17/3
Since we are dealing with whole numbers (as animals cannot be divided), the maximum number of dogs in the yard is the largest whole number in the range 7/3 ≤ d ≤ 17/3, which is 5.
Therefore, the greatest possible number of dogs in the yard is 5.