yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Solving equations and inequalities through substitution example 3


2m read
·Nov 11, 2024

Joey is training for a hot dog eating contest. The person who eats the most hot dogs in 10 minutes is the winner. If r is the number of hot dogs that Joey can eat in a minute and n is the total number of hot dogs he eats in the contest, we can write the following equation.

So, this just makes sense: he eats a total of n hot dogs, and the contest is 10 minutes, so you divide that by 10. He's going to eat n hot dogs in 10 minutes, and so yes, this will give you the number of how many hot dogs on average he ate per minute.

If Joey can eat six and four-fifths hot dogs per minute, so they're saying r is six and four-fifths. How many hot dogs does he eat during the ten-minute contest? So, they're saying, hey, what is n going to be right over here?

N divided by 10 is six and four-fifths. R in this situation is six and four-fifths; that’s how many hot dogs he can eat per minute. Now, there are a couple of ways that you could tackle this.

You could say, hey, some number divided by 10 is six and four-fifths, and so you say, well, that number must be six and four-fifths times ten. Six and four-fifths times ten would be 60 plus 8 or 68. So that's one way you could do it. You're essentially multiplying both sides of this equation by 10.

The other way you could do it is you could just try out numbers, and that usually takes a lot longer. But at least it'll give you the sense of how the equation relates, and especially because they have choices here, it's not a bad idea.

If obviously the ideal one is to just think logically through it. Hey, if something divided by ten is six and four-fifths, then ten times six and four-fifths is going to be that something, and that's how you could get 68.

Or if you want, you could try out the different numbers. Look, 65 divided by 10 is only going to give you 6.5; that's not the r we're looking for. 56 divided by 10 is going to give you 5.6; not the r we're looking for.

68 divided by 10 is going to give you six point eight six or six and eight tenths, and six point and six and eight tenths is the same thing as six and four-fifths. So 68 works.

45 hot dogs, you divide that by 10, you're going to get 4.5 hot dogs per minute. So all of these are completely legitimate ways of doing it. The important thing is that you understand this relationship and you understand how these variables work with respect to each other.

More Articles

View All
15 Ways to Get Ahead of 98% of People
98% of people aren’t living up to their full potential. They form their opinions based on superficial things that they hear. They can’t manage themselves, but they also don’t think enough about themselves, what they want, and what makes them happy. All of…
The 'Great Rotation' is Here.
For more than two years, the primary theme that we’ve seen in the stock market has been a small selection of large cap technology names leveraged to AI and semiconductors driving the stock market forward: Apple, Amazon, Nvidia, Meta, Google, Microsoft, Te…
2015 AP Calculus BC 2d | AP Calculus BC solved exams | AP Calculus BC | Khan Academy
Find the total distance traveled by the particle from time t equals zero to t equals one. Now let’s remember, they didn’t say find the total displacement; they said find the total distance traveled by the particle. So if something goes to the right by on…
🌍 Which Planet is the Closest?
My Very Easy Method Just Speeds Up Naming… Planets. Every Physics classroom has a Solar System line like this. Or… like this. (Sorry, Pluto.) Looking at the line, which planet is closest to Earth: Venus or Mars? To answer, you need first know that, like …
Horses vs. Horsepower: Watch Historic Rides Race Each Other | National Geographic
History is important, and we get hundred-year-old vehicles out and run. We feel that the educational aspect of someone being able to see these cars in motion is well beyond what someone would learn simply by watching the cars in a museum. Welcome to Race…
The Firefighting-inspired Watch #shorts #watch
I should disclose right now then, so we actually make the watches, Kevin, from genuine upcycled firefighting materials. Even elements of the case, which you can see by the striking strap that you have on your wrist. Yes, I should disclose right now that I…