The ratio of blue to black denims at a certain shop is 15:16. If there

We can actually solve this question WITHOUT using the information in the second sentence.

The ratio of blue to black jeans at a certain shop is 15:16
There are many possibilities. Here are a few:
- There are 15 blue jeans and 16 black jeans
- There are 30 blue jeans and 32 black jeans
- There are 45 blue jeans and 48 black jeans
- There are 60 blue jeans and 64 black jeans
- There are 75 blue jeans and 80 black jeans
etc

Notice that, since the number of each type of jeans must be an INTEGER, the number of blue jeans must be a multiple of 15

Check the answer choices....only one answer choice is a multiple of 15

Answer:

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Given :
Initial ratio of Jeans (Blue:Black = 15x:16x)
Final ratio of Jeans (Blue:Black = 15x:21x)

Hence difference of 21x - 16x is caused by the addition of the 35 black jeans, x = 7.
Hence the blue jeans is 15x = 105(Option C)
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Let number of Blue jeans be \(= X\)

Let number of Black jeans be \(= Y\)

Blue jeans / Black jeans \(= \frac{X}{Y} = \frac{15}{16}\)

\(Y = \frac{16}{15} * X\) --------- (i)

Blue jeans / Black jeans + 35 additional black jeans \(= \frac{X}{Y + 35} = \frac{15}{21}\)

\(\frac{X}{Y + 35} = \frac{15}{21}\)

\(21 X = 15 (Y + 35)\)

\(21 X = 15 Y + 525\) ---------- (ii)

Substituting value of Y from (i) in (ii), we get;

\(21 X = 15 (\frac{16}{15} * X) + 525\)

\(21 X = 16 X + 525\)

\(21 X - 16 X = 525\)

\(5 X = 525\)

\(X = \frac{525}{5} = 105 .\) Answer (C) ...

The ratio of blue to black jeans at a certain shop is 15:16. If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21. How many blue jeans does the shop have?

Let Blue/Black original value, \(\frac{15}{16}\)= \(\frac{15x}{16x}\)
By data,
16x=16x+35
\(\frac{15x}{16x+35}\)=\(\frac{15}{21}\)
Solving above, x=7
Blue= 15x=15*7=105
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15 + 16 = 31
15 + 21 = 36

SO, 5 represents 35 Black jeans or 1 represents 7 Black jeans , as no blue jeans were added...

So, the total number of blue jeans is 15*7 = 105 Blue Jeans...

Answer will be (C)
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Blue/Black (x/y)=15\16
If additional 35 black jeans are added the ration becomes
(x/y+35)=15/21

Solving for X and Y We get number of blue jeans 105

We are given that the ratio of blue to black jeans at a certain shop is 15x : 16x. We are also given that if there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15 : 21. Thus:

15x/(16x + 35) = 15/21

15x/(16x + 35) = 15/21

15x(21) = 15(16x + 35)

21x = 16x + 35

5x = 35

x = 7

Thus, the shop has 15(7) = 105 blue jeans.

Answer: C

(Note: We also could have recognized that the number of blue jeans must be a multiple of 15 and the only answer choice that is a multiple of 15 is answer choice C, 105.)
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Here's a solution that uses two variables:

The ratio of blue to black jeans at a certain shop is 15:16
Let B = number of blue jeans PRESENTLY in the shop
Let K = number of black jeans PRESENTLY in the shop
So, we can write: B/K = 15/16
Cross multiply to get: 16B = 15K

If there were 35 additional black jeans in the shop, the ratio of blue to black jeans would be 15:21.
So, B = number of blue jeans in the shop AFTER 35 black jeans are added
And K + 35 = number of black jeans in the shop AFTER 35 black jeans are added
So, we can write: B/(K + 35) = 15/21
Cross multiply to get: 21B = 15(K + 35)
Expand: 21B = 15K + 525
Subtract 525 from both sides to get: 21B - 525 = 15K

How many blue jeans does the shop have?
We now have the following system of equations:
16B = 15K
21B - 525 = 15K

Since both equations are set equal to 15K, we can write: 16B = 21B - 525
Subtract 21B from both sides: -5B = -525
Divide both sides by -5 to get: B = 105

Answer:

Cheers,
Brent
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Why did we add X to the numerator and denominator in the fraction?

it took time to solve this question but i was able to make out that answer choice will be multiple of 5, having see the numbers... 35 and 15. and choose C correctly.

Answer will remain a multiple of 15. Because there is no change on that one.
Hence C
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