Solve The Problem?

Question

Chandra has 2 liters of a 7% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of 42% solution?

a. 5 liters of 57% solution
b. 5 liters of 56% solution
c. 5 liters of 54% solution
d. 5 liters of 59% solution

Answer 1

Using pearson square. draw a square (.... is for spacing)

.............___________
7%...... |
.............|
.............|
.............|
x%........|
.............|___________


Write final percent solution in the center. Diagonally Subtract.

.............___________ (x-42)
7%...... |
.............|
.............|..............42
.............|
x%........|
.............|___________ 42-7= 35

Ratio 1: The amount of 7% is x-42 / (x-42)+35 or 2 liters /7 liters

Ratio 2: The amount of x% is 35/ (x-42)+35 or 5 liters/7 liters


set up a ratio (either one would work).

35 / x-7 = 5/7

35*7=5*(x-7)

280 = 5x
x=56

Try b

Answer 2

if you start with 2 L. and end with 7 L., obviously you add 5 L. So
pct x amt + pct x amt = pct x amt.
7(2) + x(5) = 42(7)
5x = 42(7) - 2(7) = 40(7) = 280
x = 56%
answer b.