Question

A pharmacist has a 13 % alcohol solution and another 18 % alcohol solution. How much of each must he use to make 50 grams of a 14 % alcohol solution?

Answer 1

A pharmacist has 40 grams of 13% alcohol solution and 10 grams of 18% alcohol solution.

To find :

How much of each must a pharmacist use to make 50 grams of a 14% alcohol solution?

Given :

A pharmacist has a 13% alcohol solution and another 18% alcohol solution.

13% = $\frac{13}{100}$ = 0.13

18% = $\frac{18}{100}$ = 0.18

Let, 13% of alcohol solution be 0.13 x.

      18% of alcohol soluton be 0.18 (50 - x).

      50 grams of a 14% of alcohol solution be $\frac{14}{100}\times50$ $= 7$.

Add 13% of alcohol and 18% of alcohol and equate to 50 grams of a 14% of alcohol solution.

0.13 x + 0.18(50 - x) = 7

0.13 x + (0.18 × 50 - 0.18 x) = 7

0.13 x + 9 - 0.18 x = 7

9 - 0.05 x = 7

9 - 7 = 0.05 x

2 = 0.05 x

0.05 x = 2

x = $\frac{2}{0.05}$

x = 40.

Where, x = 40

            50 - x = 50 - 40 = 10

Therefore, 40 grams and 10 grams.

To learn more...

1. A pharmacist has a 13 % alcohol solution and another 18 % alcohol solution. How much of each must he use to make 50 grams of a 14 % alcohol solution?

brainly.in/question/15240605

2. How much pure alcohol must be added to 400 ml of a 15% solution to make its strength 32%

brainly.in/question/4512043

Answer 2

Answer:

The quantity of 13 % alcohol in 50 gm is 40 gm

The quantity of 18 % alcohol in 50 gm is 10 gm  .

Step-by-step explanation:

Given as :

The percentage of alcohol solution = 13%

The percentage of another alcohol solution = 18%

Let The quantity of 13% alcohol = x gram

Let The quantity of 18% alcohol = y gram

Total quantity after adding both = 50 gram

The percentage of mixture = 14% alcohol

According to question

∵ Total quantity = 50 gm

So, x + y = 50                 .......1

Again

13 % of x + 18 % of y = 14 % of 50

i.e $\dfrac{13}{100}$ × x + $\dfrac{18}{100}$ × y = $\dfrac{14}{100}$ × 50 + $\dfrac{14}{100}$ × 50

Or,  13 x + 18 y = 700            .........2

From eq 1 and  2

(13 x + 18 y) - 13( x + y) = 700 - 13 × 50

Or, (13 x - 13 x) + (18 y - 13 y) = 700 - 650

Or, 0 + 5 y = 50

∴     y = $\dfrac{50}{5}$

i.e y = 10

So, The quantity of 18 % alcohol in 50 gm = y = 10 gm

Put the value of y in 1

So, x + y = 50

Or, x = 50 - y

i.e x = 50 - 10

i.e  x = 40

So, The quantity of 13 % alcohol in 50 gm = x = 40 gm

Hence, The quantity of 13 % alcohol in 50 gm is 40 gm

And The quantity of 18 % alcohol in 50 gm is 10 gm  . Answer