Hi Brent,
Thank you for the explanation. That does make sense, I guess I figured that when I set up an equation and get a value for n/p that will only result in one possible value.
How is this question different from say something like the below?
"On Monday, a class has 8 girls and 20 boys. On Tuesday, a certain number of girls joined the class just as twice that number of boys left the class, changing the ratio of girls to boys to 7 to 4. How many boys left the class on Tuesday?"
Because in the the above problem you can simply set up an equation to equal the new proportion to determine what the original proportion was.
girls = boys = 8+x/20-2x = 7/4 to determine what x is and therefore what x, the number of girls, is and use that to solve for what the number of boys is.
Is the reason the girls and boys question is different than the pen and pencil question because in the former there's a relationship identified between girls and boys (boys = 2*girls) whereas in the pen and pencil question there is not relationship identified between the two values other than the proportion which allows the proportion to be any multiple of 47/17.
Apologies for all the back and forth and for so many questions, but I really appreciate you explanations!
Thank you very much again!
GREStudent2020 wrote:
@GreenlightTestPrep
Hi Brent,
Please see my steps below. (n = pen and p = pencil)
n+5/p+3 = 47/17
17n + 85 = 47p + 141 (subtract 85 from both sides)
17n = 47p + 56 (divide both sides by 17)
n = 47p/17 + 56/17 (divide both sides by p to get n/p since the question asks for the original proportion value)
n/p = 47/17 + 56/17 (add fraction)
n/p = 103/17
I think I might have caught my mistake as I was typing my steps out. When I divide both sides by p, I would also have to divide the 56 by p, correct? I didn't do that above so maybe that's where I made my first mistake?
Additionally, you said I should get 17n = 47p + 56. Which I did in step 3. How would I proceed after that step to get the value of the original proportion, n/p?
Thank you in advance!
Yes you correctly identified your mistake.
If we take: n = 47p/17 + 56/17
And divide both sides by p, we get: n/p = 47/17 + 56/17p
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Once we get to the equation 17n = 47p + 56, we might recognize that there are infinitely many solutions.
If we're able to identify pairs of INTEGER values of n and p that yield different values for Quantity A, then we're done.
However, that could be quite time-consuming.
A faster approach is to do what I did in my solution.
If we know that (n+5)/(p+3) = 47/17, then it's also true that (n+5)/(p+3) = 94/34 (since 47/17 and 94/34 are equivalent fractions)
We could also have (n+5)/(p+3) = 940/340 or (n+5)/(p+3) = 9400/3400
etc
So one possible situation is n+5 = 47 and p+3 = 17, in which case n/p = 42/14 = 3/1
Another possible situation is n+5 = 94 and p+3 = 34, in which case n/p = 89/31
Another possible situation is n+5 = 940 and p+3 = 340, in which case n/p = 935/337
etc
Does that help?[/quote]