We're going to solve some application problems now that involve percent, and the solution to these application problems will require
that we translate each of the applications into one of our three basic percent problems. And as you know from the last section,
it's very easy to solve them once they're in this form because we just do a direct translation; an equation comes out of that;
we solve the equation: there's our solution. Let's look at our first application: "On a 120-question test, a student got 84 correct answers.
What percent of the problems did the student work correctly?"
So, what I want to do is take this problem right here and translate it into one of my three basic percent problems.
The student took a 120-question test; they got 84 correct answers. And what we want to know is,
what percent of the problems did the student work correctly? So, what we want to know is, 84 is what percent of 120? So, let's write that down:
84 is what percent of 120? Now, isn't that the same as what this problem is asking for? We have a 120-question test;
the student gets 84 correct answers; and we want to know, what percent of the problems did the student work correctly.
So really, what we want to know is, 84 is what percent of 120? So, we have translated this correctly. Now, solving it's no problem for us.
So, 84 is what percent of 120? So, there's our equation. To solve that, divide both sides by 120. I do that division.
And let's see, 84 ÷ 120: on a calculator, what'd I get? 0.70 = n. So, n is going to be equal to 70%.
So, if a student takes a 120-question test and get 84 correct answers, they've answered 70% of the questions correctly
because 84 is 70% of 120. So, let's go to the next board now and work the next of these application problems.
Problem 2: we say, "How much HCL (hydrochloric acid) is in a 60-milliliter bottle that is marked 75% HCL?"
So, what I have is a bottle that has 60 milliliters of solution; 75 percent of it is HCL.
So, what I want to know is how many milliliters of HCL are in the 60-milliliter bottle. So, what I want to know is this:
what is 75% of 60? So, that's my question: what is 75% of 60?
And that's a direct translation of this problem into one of my three basic percent problems. Now to solve this problem,
I simply translate into an equation; solve the equation, and away we go.
So, what or what number is going to be n; is is equal; 75 percent is 0.75 times 60? So, I have n equals 0.75 times 60.
I do that multiplication on a calculator, and I get n is equal to 45. And then, I'm going to put in my units: milliliters.
So, if I have a 60-milliliter bottle and it's marked 75% HCL, that means that 75 percent of what's in there is hydrochloric acid.
So, if I want to know the amount of hydrochloric acid, I can ask myself this question: what number is 75% of 60? The answer to that is 45.
And that's the number of milliliters of HCL in a 60-milliliter bottle that's marked 75% HCL. Let's try one more problem.
If, let's see, it says, "Suppose 60% of the graduating class in a certain high school goe" (g-o-e! how about,) "goes on to college.
If 240 students from this graduating class are going on to college, how many students are there in the graduating class?"
So, let's see. We know 240 students are going on to college and that's 60% of the graduating class.
What we want to know is, what is the size of the graduating class? So, what we're going to ask is this: 240 is 60% of what number?
So, I translate this: 240 = 60%, 0.60; "of what number" will be 0.60(n). Divide both sides by 0.06. And then, I end up with, let's see,
240 ÷ 0.60, that comes out to be 400. So, I end up with n = 400. So, there must be 400 students graduating in the school
if 240 of them go on to college and 240 is 60% of the graduating class. So, this is a kind of a long application problem.
But after you read it through a couple of times, you'll see the question that's being asked is this: 240 is 60 % of what number?
So, I translate that into an equation; solve the equation; I have the answer to my problem: 400 students.