Question

A scientist mixes water (containing no salt) with a solution that contains 35 % salt. She wants to obtain 210 ounces of a mixture that is 30 % salt. How many ounces of water and how many ounces of the 35 % salt solution should she use?

Answer 1

ANSWER:

She should use 30 ounces of water and 180 ounces of 35% salt.

SOLUTION:

First, let us set up a table and fill in the unknowns with variables x and y.

component     Unit Value    Amount( ounces)   value

0% salt                0.0                 x                            0.0x=0

35% salt                0.35                 y                            0.35y

Total Mixture          0.3               210                            0.3×210=63

From this, we can easily set up the two equations.  

Sum of values of two salts = Value of mixture  

0x+0.35y = 63  ................(1)

0.35y = 63  

$y = \frac{63}{0.35}$

y = 180

Now,

Sum of amounts of each salt = Amount of mixture  

x + y = 210 ---------> (2)

so, put y = 180 in (2)

x + 180 = 210  

x = 210 – 180  

x = 30

Hence, she should mix 30 ounces of water and 180 ounces of 35% salt.