Question

Gabe, a nuclear physicist need 60 L of a 60% acid solution he currently has a 50% solution and a 70% solution how many liters of each does he need to make the needed 60 L of 60% acid solution Gabe needs ___ liters of the 50% solutionit says he also needs __ liters of the 70% solution

Answer 1

30 liters of 50% solution and 30 liters of 70% solution.

1) We can solve this problem, making use of an equation.

x- the amount of 70%

60 -x stands for the amount of 50% solution. From this we can write the following equation, rewriting the percentages as decimal numbers:

`\begin{gathered} 0.5(60-x)+0.7x=0.6(60) \\ 30-0.5x+0.7x=36 \\ 0.2x=36-30 \\ 0.2x=6 \\ (0.2x)/(0.2)=(6)/(0.2) \\ x=30 \end{gathered}`

Note that we equated two equations, the first one:

`0.5(60-x)+0.7x`

provides the amount of 50% solution minus that 60L and the second one yields 60% of those 60 Liters, so with x, we get the remaining amount of that 50% solution.

b) Since the other question refers to the amount of of the 70% solution and we also know that Gabe needs 30 liters of the 50% solution we can write the following, calling the second amount as y:

`\begin{gathered} 30+y=60 \\ y=60-30 \\ y=30 \end{gathered}`

Note the total of 60 Liters

2) Thus the answer is 30 liters of 50% solution and 30 liters of 70% solution.