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CAHSEE Math 4.1 Mathematical Reasoning 198 Views


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Description:

Mathematical Reasoning Drill 4 Problem 1. Approximately how many gallons of paint is needed if eight people paint the wall together for an hour?

Language:
English Language

Transcript

00:02

Here’s another shmoop du jour for you and your brain...

00:06

The governor of New York has decided to build a Not-So-Great-Wall-of-China…town.

00:11

Of course, he wants to make it stand out, so he feels it should be colorful…

00:16

The following graph shows the relationship between the number of gallons of paint needed

00:19

to cover a wall, and the size of the wall (in square feet). 

00:23

It is estimated that an average person can paint 120 square feet of wall space in an hour.

00:29

Approximately how many gallons of paint

00:31

is needed if eight people paint the wall together for an hour?

00:35

And here are the potential answers...

00:42

The first thing we have is a graph that tells us how much paint it takes to cover a certain

00:46

number of square feet in area.

00:49

Then, we’re asked to find how much paint eight people would need to paint at full capacity

00:53

for an hour. The question tells us how much one person can paint in an hour…

00:59

…so to find out how much area is covered by eight people, we can just multiply that by eight.

01:05

8 times a 120 is 960…

01:08

…so we know that in an hour, eight people can cover 960 square feet with paint.

01:14

Now, we just have to convert 960 feet into the number of gallons of paint we’ll need.

01:20

But since we don’t have exact numbers, we’ll have to estimate a little bit.

01:25

The easiest way to do this on a graph is to look at intersections.

01:28

We can see that the y-coordinate of 900 square feet is about equal to 2.5 gallons of paint…

01:33

…and the x-coordinate of 3 gallons of paint is about the halfway mark between 900 and

01:38

1200 square feet covered, which is roughly 1050 square feet.

01:44

We know that 960 is between 900 and 1050,

01:48

so our x-coordinate has to be greater than 2.5 and less than 3.

01:52

The only answer choice that meets those criteria is (B), 2.7 gallons.

01:56

As in… “Brown might have been better.”

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