Math systems of solution

Question

A scientist has two solutions, which she has labeled solution a and solution b. Each contains salt. She knows that solution a is 70% salt and solution b is 95% salt. She wants to obtain 150 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?

Answer 1

Let me remind you first with the basic of this problem. To get the amount of salt in a mixture, multiply the amount of mixture with the percentage of salt.

Amount of Salt = (amount of mixture)(percentage of salt)

Now let's do the representation:

Let x = amount of mixture in solution a in ounces. then

150-x = amount of mixture in solution b in ounces.

Therefore:

(70%)(x)=.7x= amount of salt in solution a

(95%)(150-x)=.95(150-x) = amount of salt in solution b

(85%)(150)=127.5 = amount of salt you want to obtain.

Solution:

Now let's form the equation:

.7x + .95(150 - x) = 127.5

.7x +142.5 - .95x = 127.5

.7x -.95x =127.5 - 142.5

-0.25x = -15

x = 60 ounces for solution a

150 - x = 90 ounces for solution b

Answer 2

The key to solving this problem is using systems of equations.

a(0.70) + b(0.95) = 150(0.85)

a + b = 150

Systems are usually solved using either the substitution method or elimination method. Based on the setup of this problem, substitution would be easier. I want to substitute the "a" variable. The "b" variable could be substituted as well; it's your choice. Both paths will lead to the same answer.

Isolate "a" in the second equation

a + b = 150

a = 150 - b

Substitute "a" into the first equation

(150 - b)(0.70) + b(0.95) = 150(0.85)

Solve for "b"

(150*0.70) - 0.70b + 0.95b = 127.5

105 - 0.70b + 0.95b = 127.5

105 + 0.25b = 127.5

0.25b = 127.5 - 105

0.25b = 22.5

b = 90 ounces

Use the value of "b" to solve for "a"

a = 150 - b

a = 150 - 90

a = 60 ounces