Question

please help!

You need a 15% acid solution for a certain test, but your supplier only ships 5% solution and 17.5% solution. If you need 20 liters of 15% acid solution, how many liters of 5% and 17.5% solution do you need?

Answer 1

Answer:

4 liters of 5% solution and 16 liters of 17.5% solution we need.

Step-by-step explanation:

Let us assume that x liters of 5% solution and y liters of 17.5% solution are taken.

So, x + y = 20 ........ (1)

As the final solution is of 15%, so we can write

$\frac{\frac{5x}{100}+ \frac{17.5y}{100}}{x + y} = \frac{15}{100}$

⇒ 5x + 17.5y = 300 ......... (2)

Now, solving equations (1) and (2)  we get,  

17.5y - 5y = 200

⇒ 12.5y = 200

⇒ y = 16 liters

Hence, x = 20 - y = 4 liters.

Therefore, 4 liters of 5% solution and 16 liters of 17.5% solution we need. (Answer)

Answer 2

Answer:

4 liters of 5% solution and 16 liters of 17.5% solution we need.

Step-by-step explanation:

Let us assume that x liters of 5% solution and y liters of 17.5% solution are taken.

So, x + y = 20 ........ (1)

As the final solution is of 15%, so we can write

⇒ 5x + 17.5y = 300 ......... (2)

Now, solving equations (1) and (2)  we get,  

17.5y - 5y = 200

⇒ 12.5y = 200

⇒ y = 16 liters

Hence, x = 20 - y = 4 liters.

Therefore, 4 liters of 5% solution and 16 liters of 17.5% solution we need. (Answer)