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.
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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
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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?

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.

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.

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