Sam S. answered • 10/17/21
Specializing in Test Prep and Writing
Hi, Jenson,
I'm don't know if you're looking for a specific format with regard to Polya's strategy, but I can walk you through the steps as best I can.
- Understand the problem
We're trying to figure out the number of people in this 10-person group that took a side trip to Hong Kong.
We know
A: the amount of money paid by people who went to HK (25,000 php)
B: the amount of money paid by people who didn't go to HK (20,000 php)
C: The number of both people who went or didn't go to HK (10 in total)
D: The total amount of money collected (230,000 php)
We will need to create an equation into which we can plug our number (the number people who went to HK), and get the collected money back. What's more, we will need to find a way to express the number of people who didn't go to Hong Kong in terms of people who did. To that end, let's go on to step 2.
- Make a plan.
We're going to need to make an equation that expresses what we know. Basically, our equation needs to say this:
Money collected = HK-travelers * HK-money + non-HK-travelers * non-HK-money.
We know all of this information, except for the HK and non-HK travelers (who I will represent as x and y).
Plugging this all in, we get:
230,000 php = x * 25,000 php + y * 20,000 php.
But now we've hit a snag: how will we solve for x and y at the same time?
The answer is to express y in terms of x. Remember that every person who didn't go to HK is one fewer person who did. Since there are 10 people on this trip, we can say:
y = 10-x.
The number of people who didn't go to HK is 10 minus the people who did. Let's plug this into our original equation.
230,000 = 25,000*x + 20,000 * (10-x)
Awesome! Now let's solve this.
- Execute the plan.
We have our equation. Now all we need to do is work through it. First, let's get this in as simple of a form as possible.
230,000 = 25,000*x + 20,000*(10-x) boils down to
230,000 = 25,000*x + 200,000 - 20,000*x, which boils further down to
230,000 = 5,000*x + 200,000
Starting to look easier? Great! Now let's solve for x. To start, let's subtract 200,000 from both sides
230,000-200,000 = 5,000*x + 200,000 - 200,000
30,000= 5,000*x
Now we can divide by 5,000 on both sides!
x = 30,000/5,000
x= 6
There are 6 people who took a trip to Hong Kong. Now let's double-check to be sure.
- Reflect and check.
We think 6 people went to Hong Kong. Given that there are 10 people in total, that means there are 4 people who didn't go. Remember our equation that we set up in the beginning?
Money collected = HK-travelers * HK-money + non-HK-travelers * non-HK-money.
Let's actually try and calculate the money collected using our new knowledge. To do that, we'll pretend we don't know how much money was collected, then plug in the answers we got into our equation!
25,000*6 + 20,000*4 = money collected.
If we do the math, we get 230,000 php! We were right.
So to reiterate, we:
A: Broke the problem down, figured out what we knew, and figured out what we needed to know.
B: Took a look at what we knew and generated an equation to describe our knowledge.
C: Used what we knew in this equation to solve for what we needed to know.
D: Used the answer we got as part of our original equation to ensure that it was right.
And given this, we know that 6 people took the side trip to Hong Kong.
I'd recommend going through this on your own, using this as a guide, and see if you can get the answer by yourself. If you have a teacher who wants this written down in a specific way, you'll also be able to get this to fit their guidelines better.
Hope this helped!
