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

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 = (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.