Math 115 Maybelline Gonzalez

The Story

John Einstein wasn’t a scientist, hell he despised science so how did he wind up working in a science lab as an intern you ask? Easy, his guidance consoler had made a terrible mistake. The money he made was the only reason he had not quit this job or else he would have quit a long time ago. His boss was an old corpulent man named Dr. Lee Cunningham who worked diligently in his small lab.

John hardly ever spoke to Cunningham since the doctor was often busy with his work. Everyday he would leave John a note of instructions of what he needed to do for the day but I digress. Anyway this day however, the doctorwas working with certain acid concentrations that where highly dangerous which compelled him to ask John to assist him today. Poor unwaryJohn had just finished his rounds for the day and was about to leave when the good doctor walked up to him and said “Mr. Einstein would you care to assist me today?” “With what?” asked John surprised that the old man was speaking to him and asking for his help. “Follow me” replied Cunningham but John was not interested in helping him in the slightest.

“I’ve done my work and…”

“I could replace you!” The doctor interrupted annoyed with the young man.

“Then do” John said angrily “I quit!”

“I will pay you for overtime John”

And without hesitation John replied “I’ll do it then”

The doctor smiled to himself and told his assistant to follow him to a small table. The table held two test tub of acid solution and one beaker of acid. John examined the tubs then looked toward the old man.

“What am I suppose to do”John asked the doctor.

Cunningham dug into his coat pocket and gave his assistant a pen and paper. He told him sit on a small chair and empty table located in the back of the lad. John quickly sat down and toke notes as the old man spoke.

“I want you to make ten1iters of forty percent acid solution. There are fifty and twenty five percent of acid solutions in stock so you need to mix enough of each liter to obtain forty percent.”

“What?” repliedJohnunintelligently, dropping his pen and gazing at the doctor with a confused expression. Cunningham did not seem to notice John’sfacialexpression and proceeded to walk towards the other end of the room.

“John” Yelled the doctor“I would be careful not to add to much or too little of the solutions!”

“What would happen if I do?”John asked apprehensively.

“You could possible hurt yourself if you do but do not be alarmed if you know what you are doing.” stated the doctor. “However if you don’t then…”

“I just remember that I had something I forgot to do!” John interrupted and ran towards the exit.The doctor just watched him run away and said “It’s so hard to find good help these days…”

The End

The Solution to the Problem

Cunningham wanted John to make 10 liters of 40% acid solution. The solutions of 50% and 25% are in stock. So the question is how many liters of each must be mixed to prepare the solution?

Step one is to create a mathematical model: X + Y = 10

Step two is to multiply: (.40) (10) which equal 4

Step three is to multiply: (.50) (X) + (.25) (Y)

.50X + .25Y =

Step four is to multiply all numbers by 100: .50X + .25Y = 4 (100)

50X + 25Y = 400

Step five is to create a system of equations: X + Y = 10

50X + 25Y = 400

Step six is to use the method of elimination by addition by eliminating the Y

(-25) X + Y = 10-25X - 25Y = -250

50X + 25Y = 400 50X + 25Y = 400

Negative 25 and positive 25 cancel each other which leaves: 25X = 150

Step seven is to divide 25X by 150 which X = 6

Step eight is to substitute 6 for X in the original equations: X + Y = 10

6 + Y = 10

-6 -6

Y = 4

In conclusion 6 liters of 50% solution and 4 liters of 25% solution must be mixed to prepare 10

Liters of 40% acid solution.