How many apartment buildings are needed to house 3000 people if each building can house 150 peop

How many apartment buildings are needed to house 3000 people...

Key Concepts

Division

Division is a basic arithmetic operation used to determine how many groups of a certain size can be formed from a total amount. In this context, it involves dividing the total number of people by the capacity of one apartment building to find the number of buildings needed.

Capacity

Capacity refers to the maximum number of individuals or units that can be accommodated by an item or space. Here, it relates to the limit of people that each apartment building can house, which is essential for planning how many buildings are required.

Ceiling Function

The ceiling function is a mathematical concept used to round numbers up to the nearest whole number. When a division results in a fraction, this function ensures that the number of units (in this case, apartment buildings) is sufficient to cover the entire need, since partial units are not practical.

Transcript

0:00 Hello.

00:01 So here we're told we have this apartment complex that has 230 apartments.

00:05 They're having either one, two, or three bedrooms.

00:08 So the number of one bedroom apartments is 10 more than three times the number of three bedroom.

00:16 Okay, so let's let x be one bedroom, let's say y be two bedroom, and let's say z be three bedroom.

00:23 So then we have that x plus y plus z.

00:26 That's going to be equal to 230 apartments.

00:29 So what's about the next part of the question? we're giving the next part of information here says that the number of two bedroom apartments.

00:38 So that's going to be y is, so y is, equals 10 more than three times the number of three bedroom apartments.

00:47 So three times the number of three bedroom apartments, that's going to be 3z.

00:53 But then 10 more than that, so plus 10.

00:56 So 3z plus 10 is going to be equal to y.

00:59 And then we also know the number of one bedroom apartments is twice the number of two bedroom apartments.

01:05 So therefore, number of one bedroom apartments, which is going to be x is or equals two times the number of two bedrooms or two y.

01:13 Okay.

01:13 So now we know what x is, right? x is equal to two y.

01:19 We know what y is in terms of z.

01:22 So we can say that, so what we could do is just to have everything in terms of why, we could solve this second equation for z in terms of y.

01:43 So if y is equal to 3z plus 10, that means that z is going to be equal to what? it's going to be equal to y, well, 3z is going to be equal to.

01:55 To y minus 10 so therefore we get that z we just divide everything by three and get that z is going to oops z is going to be equal to uh y minus 10 over three okay so now we have everything um basically in terms of why we know the x plus y plus z is 230 what is x x is 2y so we'd have two y so we'd have two y plus y plus z what is z is z is y minus 10 over 3 is going to be equal 2 is going to be equal to 230 okay well once we have this we can go ahead and solve this for y 2y plus y is going to be 3 y so 3y plus well y minus 10 over 3 we could get a common denominator of 3 for the left side so we get 3 y is going to be as 9 y over 3 so we get 9y over 3 plus y minus 10 over 3 is equal to 230.

03:09 This gives us 9y plus y plus y minus 10.

03:12 So 9 .1 plus y is 10 y to get 10 y minus 10, all over 3 is going to be equal to 230...

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