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# Analyzing structure word problem: pet store (1 of 2)

Sal solves a word problem about the unknown number of bears, cats, and dogs in a pet store. This is part 1 where Sal uses a visual reasoning. Created by Sal Khan.

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• Could you not also input the lowest possible numbers like 1 bear over 3 cats 2 dogs and 1 bear ( 1b / 3c+2d+1b) to figure out an answer depending on what yo wanted to find. so 1 bear would be 1 over 6 or would the 1 bear on the numerator cancel out the bear on the denominator?
• no because you cant cancel the bear out because their is addition going on
1/ 3*2*1 USES MULTIPLICATION-you can use it then
• I don't think that it makes any logical sense. Think of it as a common sense problem. Can someone explain?
• Here is how I thought about it. 1/3 is the same as 1/1+1+1 and we can replace 1 with a variable that represents an arbitrary number of units. In this case if we went with b like the problem in the video, we would get a ratio of b/b+b+b in order to be equivalent to 1b/3b, or 1/3 when simplified.

Though since d>b and c>d, we know that the denominator, c+d+b, has to be larger than 3b and when you increase the denominator while keeping the numerator the same you end up with a smaller fraction - for example 1/3 compared to 1/6, which is the largest possible ratio that b/c+d+b could be if we went with the least possible number of animals (1b, 2d, 3c).
• that's only true if a, b, and d were all consecutive integers (odd or even).
because a>d>b could be 5>2>1 which is 2/ 8 which is 1/4 not 1/3
?
• Well, you have answered your question yourself here, the question is not an equality statement but rather a question of what is bigger or smaller to another thing. In this case, c>d>b, you suggest the combination 5>2>1 the equation is b/c+d+b which would be 1/1+2+5 = 1/8, and 1/8 is definitely smaller than 1/3. Hope that helps :)
• Where can I find a video that shows how to plot linear inequalities for coordinates?? Thanks
• Why is the question about bears rather than, for instance, bunnies?
• bears are just better
• if c>d>b, then c equals b plus something, b+x, and d equals b plus something, b+y. Then our expression turns into: b/(b+x)+(b+y)+b which is the same as b/3b+x+y deviding by b we get: 1/(3+(x/b)+(y/b)), and since the denominator is 3 plus something and all variables are positive, we conclude (3+(x/b)+(y/b)) is bigger than 3, and therefore 1/(3+(x/b)+(y/b)) is smaller than 1/3.
• That is correct. Using the given information that c > d > b, we can express c and d in terms of b, as c = b + x and d = b + y, where x and y are positive numbers. Substituting these expressions into the given expression, we get b/(b+x) + (b+y) + b = b/3b+x+y.

Dividing both sides by b, we get 1/(3+(x/b)+(y/b)). Since x/b and y/b are positive, (x/b)+(y/b) is positive, and so 3+(x/b)+(y/b) is greater than 3. Therefore, 1/(3+(x/b)+(y/b)) is less than 1/3.

Hence, we have shown that the given expression is less than 1/3, given the assumption that c > d > b.
(1 vote)
• How can we tell how much greater the #dogs is to the # bears?
• You can't, at least not from the information given in this video. All we know are that there are more dogs than bears, not how many more.
• Can I say that,

since c > d > b, then c+d >> b, (">> = much greater")

and since we have c+d+b in the denominator this will be

c+d+b >> c+d , and therefore b/c+d+b < 1b/3b .

Since the c+d+b in the denominator, there for the value will be smaller .

Thank you
• Yes, your reasoning is correct. Since c > d > b, we can conclude that c + d >> b. Therefore, c + d + b is much greater than c + d, which implies that b / (c + d + b) is less than b / (c + d). Since b / (c + d) is equivalent to b / 3b + x + y, we can conclude that b / (c + d + b) is less than b / (3b + x + y). And since the denominator 3b + x + y is greater than 3, we can conclude that b / (c + d + b) is less than 1/3.
(1 vote)
• We have dogs(D) and cats(C). There are more dogs than cats and there are at least one cat.

Compare the expressions C/C+D and 0.4. Which statement is correct? =, > or <

The correct answer say there are not enough informations.

But i want to know how to express the thought that its not C/C+D = 2/5? are they the same ratio?

My thought was that the two expressions convey the same meaning and i realize that the quantity of the variables might be different.
• I usually assess these types of problems by trying different values for the variables.
Your problem tells you there is at least 1 cat. So, C = 1, 2, 3, 4, etc.
And, there are more dogs than cats.
The only way to get c/(c+d) = 2/5 would be for c=2 and d=3 (or multiples of these)
But, you could do c=1; d=2. In this case: c/(c+d) = 1/3 (smaller than 2/5)
And, we could also do c=4; d=5. In this case: c/(c+d) = 4/9 = 0.444... with 4 repeating. So, it is now larger than 2/5.
Hopefully you can see from these examples that depending on the values of C and D, all the possibilities are correct. This is why there is not enough info.

Hope this helps.