Substitution/ System of Equations help?

Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is
35%
salt and Solution B is
95%
salt. She wants to obtain
180
ounces of a mixture that is
55%
salt. How many ounces of each solution should she use?

Answer 1

We need to write these as a system of equations. I will represent the amount of Solution A as "a", and the amount of Solution B as "b". She wants a total of 180 ounces of a mixture. Therefore,

a + b = 180

 

Now, we need to represent the same equation with the percentages of the mixture included

0.35a + 0.95b = 0.55(180)

0.35a + 0.95b = 99

 

Next, we can solve the first equation for "a", and then substitute that expression into the second equation.

a + b = 180

a = 180 - b

 

0.35a + 0.95b = 99

0.35(180 - b) + 0.95b = 99

63 - 0.35b + 0.95b = 99

63 + 0.6b = 99

0.6b = 36

b = 60

 

Now that we have a value for "b", plug that into any equation and solve for "a"

a + b = 180

a + (60) = 180

a = 120

 

Therefore, she should use 120 ounces of Solution A and 60 ounces of Solution B.