Hazel bought a paint mixture that was 30% yellow tint. She a

Question

Hazel bought a paint mixture that was 30% yellow tint. She added 6 ounces of yellow tint, and now the mixture is 40% yellow tint. How many ounces of yellow tint must Hazel add so that the mixture is 60% yellow tint?

A. 18
B. 21
C. 24
D. 27
E. 30

Show Answer

Official Answer

B

A. 18
B. 21
C. 24
D. 27
E. 30

rajdeep212003 · Answer

I approached this by taking the original mixture as x ounces.

Initially, the mixture is 30% yellow.

So yellow tint initially:
3x/10

After adding 6 ounces of yellow tint:

Yellow tint becomes:
3x/10 + 6

Total mixture becomes:
x + 6

Now the mixture is 40% yellow, so:

(3x/10 + 6) / (x + 6) = 4/10

Solving:

3x + 60 = 4x + 24

x = 36

So originally the mixture had:

30% of 36 = 10.8 ounces of yellow tint.

After adding the first 6 ounces, yellow tint becomes:

10.8 + 6 = 16.8

and the total mixture becomes:

36 + 6 = 42

Now let Hazel add y more ounces of yellow tint so the mixture becomes 60% yellow:

(16.8 + y) / (42 + y) = 6/10

Solving:

16.8 + y = 25.2 + 0.6y

0.4y = 8.4

y = 21

So the answer is:

(B) 21

The important thing here is that the question asks how much more yellow tint must be added after the mixture already became 40%, not from the original mixture.

If anyone has an even cleaner shortcut for spotting the cases quickly under time pressure, would love to hear it.

— Rajdeep

ThickGuitar · Answer

I approached this by using the alligation method

making first mixture: 30% 100%
 10 60
 40%
mixing ratio is 60:10, which is 6:1 where 6parts is the original 30% and 1part is the yellow tint we are adding to make 40%.

The problem said we added 6 ounces of the yellow tint, so using our ratio 6:1, we can find the initial ounces: 
1 part = 6 ounces, so 6 parts is therefore 36 ounces. 
this means our total ounces for the 40% mixture are 36+6=42 ounces

Making second mixture : 40% 100%
 20 40
 60%
Therefore our mixing ratio is 40:20 or 2:1
This means we need to 2 parts of the 40% we have, we are adding 1 part of pure yellow tint (100%) to make it 60%.

since 2 parts is = 42 ounces, that means we are adding 21 ounces of yellow tint.  Answer B

adewale223 · Answer

Let x be amount of paint mixture

100 - 40 = 60
40 - 30 = 10

60/10 = x/6

x = 36

Total amount 36 + 6 = 42

Answer B

Let amount of tint to be added be y

100 - 60 = 40

60 - 40 = 20

40/20 = 42/y

2y = 42

y = 21

perspiciatisearum · Answer

I prefer solving these with tracking the concentration of the part that is not being added, in this case the non-yellow as yellow is being added in both the parts.

Concenteration will decrease of the non-yellow part in the mixture when more of the yellow tint is added,we can call it 'b'.
SO initially concenteration was : yellow 30/100 and b at 70/100.
with the first addition the new concentration will be as follows.

0.70 x (old volume of mixture (X)/old volume of mixture (x) + 6oz)= 0.60 (we are given the new concenteration).

With this we can find out how much paint mixture did she initially buy and instead of a variable we will have the exact amount.

solving the eqn above we get X=36oz after the addition she has 42oz.
now we repeat the same process.

0.60 x (old volume (ie. before the addition, 42 in this case)/new volume we can call it X') = 0.40 
[0.40 because she wants to have a concentration of yellow as 60%, so the other part will become 40%)

so we have 0.60 x (42/42+x')=0.40

solving, we get X' as 21oz.

Hazel bought a paint mixture that was 30% yellow tint. She a

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Hazel bought a paint mixture that was 30% yellow tint. She a

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