A cleaning solution mixture calls for a ratio of 1 part bleach for eve

It doesn't..half as much means half less.

original ratio
1:4; 1 part bleach and 4 part water

new ratio
1/2:4; half as much bleach = 1 divided by 2 = 1/2 = 0.5 --> 0.5 parts bleach, and 4 parts water
0.5:4 = 1:8

total ammount is 27
1x+8x=27
9x=27
x=3

1x:8x = 1(3):8(3) = 3:24
bleach = 3
water = 24

very straightforward solution.

Solution:

For every 4 part of water, 1 part of bleach needed to be added.

• By mistake Aki added half of the bleach required.
• It means he added 0.5 part of bleach for every 4 parts of water.

o Let \(4x\) and \(0.5x\) be the amount of water and bleach in the solution.
o Total solution = \(4x + 0.5x = 4.5x\)
o \(4.5x =27\) Milliliters
o \(x = \frac{27}{4.5} = 6\)
• Amount of bleach in the solution = \(0.5*x = 0.5*6 = 3\) milliliter.

Hence, the correct answer is Option A.
_________________

The ratio 1 : 4, which can be re-expressed as 1x : 4x, was not followed. Instead of 1x ml of bleach, Aki used 0.5x ml of bleach.

We can create the equation:

0.5x + 4x = 27

4.5x = 27

x = 6

So, 0.5x = 0.5 * 6 = 3 ml of bleach was put in the solution.

Answer: A
_________________

A cleaning solution mixture calls for a ratio of 1 part bleach for every 4 parts water. When mixing the solution, Aki made a mistake and mixed in half as much bleach as was required by the ratio. The total solution consisted of 27 milliliters. How much bleach did Aki put into the solution, in milliliters?

(A) 3
(B) 4
(C) 6
(D) 7
(E) 8


A cleaning solution mixture calls for a ratio of 1 part bleach for every 4 parts water. so ratio of bleach: water is (1:4)

When mixing the solution, Aki made a mistake and mixed in half as much bleach as was required by the ratio.
lets consider 100 ml of solution, what is the required ratio ?
(1 parts of bleach: 4 parts of water)
amount of bleach as per required ratio = \(\frac{1}{5}*100\) = 20.
if I consider 100 ml of solution, this will contain 20 ml bleach and 80 ml water.

Aki mixed : half as much bleach as was required by the ratio; or half more than required ratio of bleach.
(1+\(\frac{1}{2}\))*20 = 30
considering 100 ml of solution again, Aki made the solution with 30 ml of bleach and 70 ml of water.
ratio of bleach per solution = \(\frac{3}{10}\)
so in 27 ml of solution, amount of bleach will be \(\frac{3*27}{10}\) = 8.1

I don't understand how "half as much" can possibly mean half more.Can someone confirm if 3 is the correct answer?

these links can be helpful in understanding the phrase 'half as much': https://www.merriam-webster.com/dictionary/half%20as%20much%2Fmany%20again%20as or https://www.macmillandictionary.com/dictionary/british/half-as-much-many-again

Read the examples carefully.
The phrase your linking is "half as much again", not just "half as much".

"Half as much again" = half original + original
"Half as much" = half original

The question uses the phrases "half as much", which refers to half the expected quantity. The links you've provided refer to the phrase "half as much again", which implies one and a half. So it seems the answer is indeed choice A.

Hi,
In my 1st attempt, I translated the question in this way and I'd highly appreciate it if anyone can point out where did I get it wrong. Thank you very much!

Required ratio Bleach/ Water = 1/4; so Bleach / total solution = 1/5 = 20%
By mistake, he poured half as much bleach as required, this mean the % of Bleach in solution = 20%/2 = 10%.
So, the amount of bleach in 27ml of solution = 27*10% = 2.7 ml

Understood that we can round-up to have the answer choice of 3ml (A). However, the percentage of bleach which I have from this approach Bleach/ total solution = 1/10 ; meanwhile in the quoted approach, the %Bleach/Solution is actually 1/9
(Bleach / Water = 0.5/4 =1/8, then Bleach/ Total solution = 1/(1+8) = 1/9)

Hence I'm not sure if my approach was wrong and where did I get it wrong?

In questions like these, should we assume that the ratio of substance 2 (in this case Water) remains unchanged unless explicitly mentioned?

Also, quick 30 seconds alternate solution:

27/4 (dividing by 4 because its 4 parts water and total solution is 27 ml) gives remainder 3 which is our answer

For 4 parts water, 1 part bleach was required. But he put only half as much so he put 0.5 parts of bleach.
Hence bleach:water = 0.5:4 = 1:8
If total solution is 9 ml, 1 ml is bleach and 8 ml is water. Since total solution is 27 ml, multiplier is 3 i.e. it has 3 ml bleach and 24 ml water.

Answer (A)
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Still, I have confusion.

How can if quantity of one part(bleach) changes from 1 to 0.5 then other part(water) remains the same(4) when total volume is same

What is the issue if I solve the problem in this way:

In the original mixture of 27 ml, the planned quantity of beach was 27/5.

On mistake the quantity should be half i.e., 27/10.

What is the issue in it ? Kindly help