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Comment on Nessa and Capri
please solve with 2 variables
Sure thing.
Sure thing.
Let N = # of CDs that Nessa has
Let C = # of CDs that Capri has
"The number of CDs that Nessa has is 14 less than twice the number of CDs that Capri has"
We can write: N = 2C - 14
"If Nessa gives 20% of her CDs to Capri, then Nessa and Capri will have the same number of CDs"
20% of Nessa's CDs = 0.2N
So, the # of CDs Nessa has = N - 0.2N
So, the # of CDs Capri has = C + 0.2N
So, we can write: N - 0.2N = C + 0.2N
Simplify: 0.8N = C + 0.2N
Subtract 0.2N from both sides to get: 0.6N = C
We now have two equations:
N = 2C - 14
0.6N = C
Take top equation and replace C with 0.6N to get: N = 2(0.6N) - 14
Simplify: N = 1.2N - 14
Subtract 1.2N from both sides: -0.2N = -14
Solve: N = 70
To solve for C, we'll use the fact that 0.6N = C
So, 0.6(70) = C
So, C = 42
TOTAL number of CDs they have = N + C = 70 + 42 = 112
Hi Brent
"The number of CDs that Nessa has is 14 less than twice the number of CDs that Capri has" We can write: N = 2C - 14
Will the Solution be same if I write: N= 14-2C
If NOT, why? And How can I know that it should be only 2C-14 and not 14-2C
Let's take it step-by-step
Let's take it step-by-step
If the number of CDs that Nessa has is TWICE the number of CDs that Capri has, we can write: N = 2C
If the number of CDs that Nessa has is 14 LESS THAN twice the number of CDs that Capri has, we write: N = 2C - 14
So, for example, if Capri has 10 CDs, then N = 2(10) - 14 = 6, which means Nessa has 6 CDs.
Likewise, if Capri has 25 CDs, then N = 2(25) - 14 = 36, which means Nessa has 36 CDs.
And if Capri has 43 CDs, then N = 2(43) - 14 = 72, which means Nessa has 72 CDs.
On the other hand, N = 14 - 2C represents a different situation altogether.
This equation suggests that the number of CDs Nessa has is equal to 14 minus twice the number of CDs Capri has.
So, for example, if Capri has 5 CDs, then N = 14 - 2(5) = 4, which means Nessa has 4 CDs.
In general, x - y is not the same as y - x (unless x = y, in which case both expressions evaluate to be 0)
Does that help?
Yes, May Be I have practice
There are definitely times in
There are definitely times in which accidentally writing x-y (instead of y-x) will yield the negative version of the correct answer. However, there will also be times when such a mistake will yield the wrong answer all together.
Another thing you can do is
C + N = 112
N = 2C - 14 (rewrite this as 2C - N = 14)
Now solve these:
C + N = 112
2C - N = 14
The N's cancel out. 3C = 126. C = 42.
Since 42 + N = 112, N=70
So we have N = 70 and C = 42.
20% of 70 is 14. 70 - 14 = 56. 42 + 14 = 56.
BOOM. There it is.
Thanks for the solution in
I have N=(2c-14)(.80) and C=1
There's a problem with your
There's a problem with your equation N=1.20c.
Just because Nessa gives 20% of her CDs to Capri, we can't conclude that Capri's CDs have increased by 20%.
For example, consider what happens if Nessa has 100 CDs and Capri has 5 CDs. This would mean that Nessa will give 20 of her CDs to Capri. So, Capri's CD collection increase from 5 CDs to 25 CDs, which represents a 400% increase (not a 20% increase).
This one is still easy enough
Since N = 2c-14
and we're looking for
N + c
= 2c-14 + c
= 3c-14
Therefore the answer after adding 14 should be divisible by 3 and only one answer choice meets this condition.
Very nice approach!!!
Very nice approach!!!
so when you multiply a side
I'm not entirely sure which
I'm not entirely sure which part of the solution you're referring to, but here are a few examples of eliminating fractions when dealing with equations:
Take the following equation: x/5 = 7
Multiply both sides by 5/1 to get: (5/1)(x/5) = (5/1)(7/1)
Expand: 5x/5 = 35/1
Rewrite the left side as follows: (5/5)(x/1) = 35/1
Since 5/5 = 1, we can write: (1)(x/1) = 35/1
And this is the same as: x = 35
Yes, this is a VERY convoluted way to solve a super easy equation. The important thing I want you to see is that the technique works because we end up with the fraction (5/5), which simplifies to be 1.
Here's another example: (2/3)(x + 1) = (1/6)(5x - 7)
Multiply both sides of the equation by 6 (aka 6/1) to get: (6/1)(2/3)(x + 1) = (6/1)(1/6)(5x - 7)
Multiply the first two fractions on each side of the equation: (12/3)(x + 1) = (6/6)(5x - 7)
Simplify the first fraction on either side: (4)(x + 1) = (1)(5x - 7)
Expand: 4x + 4 = 5x - 7
Solve: x = 11
For more information about simplifying equations involving fractions, you can watch: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...
thanks
FYI, I realized after reading
Anyway, just wanted to share with you because I thought it might be useful for you to know more specifics about what I was missing. I am understanding it better now and your comment helped a lot!
That's great that you were
That's great that you were able to identify the source of your difficulties. Your new understanding will help a lot with other similar questions.
I don't understand if they
Great question!
Great question!
This all comes down to how we defined our variables.
In this case, C = the number of CDs that Capri PRESENTLY owns.
Later, after some CDs are exchanged (resulting in Capri and Nessa having the same number of CDs), we determine that C = 42.
That is, Capri PRESENTLY owns 42 CDs, whereas the information Capri and Nessa having the same number of CDs is a HYPOTHETICAL EVENT that has not actually happened.
So, once we know that Capri PRESENTLY owns 42 CDs, we can use the other piece of information regarding the PRESENT situation (i.e., "The number of CDs Nessa (PRESENTLY) has is 14 less than twice the number of CDs Capri has") to determine the number of CDs Nessa PRESENTLY has.
Does that help?
Hi Brent, I have an algebra
If you have TWO OR MORE
If you have TWO OR MORE fractions with different numerators, we can eliminate all fractions by multiplying by the least common multiple of all the denominators.
For example: x/3 + 5/6 = x/4 + 17/6
Multiply both sides by 12 to get: 4x + 10 = 3x + 34
Solve: x = 24
If you have a fraction with just ONE fraction in front of a variable, then you can multiply both sides of the equation by the reciprocal.
For example: (2/3)x = 18
Multiply by 3/2 to get: x = (18)(3/2) = 27
Does that help?