Question

A scientist needs 0.9 liters of a 28% alcohol solution. She has available a 29% and a 26% solution. How many liters of the 29% and how many liters of the 26% solutions should she mix to make the 28% solution?

Answer 1

Given:

A scientist needs 0.9 liters of a 28% alcohol solution.

She has available a 29% and a 26% solution.

Let the number of liters from 29% solution = x

And the number of liters from 26% solution = y

so, we can write the following system of equations:

$\begin{cases}x+y=0.9\rightarrow(1) \\ 29x+26y=28\cdot0.9\rightarrow(2)\end{cases}$

Solve the system of equations to find (x) and (y)

From equation (1)

$y=0.9-x\rightarrow(3)$

substitute with (y) from equation (3) into equation (2)

$29x+26(0.9-x)=28\cdot0.9$

Solve the equation to find (x)

$\begin{gathered} 29x+26\cdot0.9-26x=28\cdot0.9 \\ 29x-26x=28\cdot0.9-26\cdot0.9 \\ 3x=2\cdot0.9 \\ x=\frac{2\cdot0.9}{3}=0.6 \end{gathered}$

Substitute with (x) into equation (3) to find (y)

$y=0.9-0.6=0.3$

So, the answer will be:

The number of liters from 29% solution = 0.6

The number of liters from 26% solution = 0.3