Question

7. How much alcohol must be added to 480 grams of hand sanitizer that is 24% alcohol to

make it a hand sanitizer that is 40% alcohol? Correct your answer to the nearest whole
number

Answer 1

the amount of alcohol to be added is 128 grams

Explanation:

Given that:

The initial mass of the hand sanitizer = 480 grams

The initial strength of the hand sanitizer = 24 %

The new strength of the hand sanitizer = 40%

The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol

First; let's find the mass of alcohol in the initial hand sanitizer;

SO;

= 24 % of 480

`=(24)/(100)*480`

= 115.2 grams

If y should represent the mass of the alcohol added to have 40%; we have

The new amount of the alcohol to be
`(115.2 + y) \ grams`

The new amount of the hand sanitizer will be
`(480 + y) grams`

∴

For the new strength of sanitizer:

40 % of (480 + y) = (115.2 + y)

`0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= (76.8)/(0.6) \\ \\ y = 128 \ grams`

Thus ; we can conclude that the amount of alcohol to be added is 128 grams