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Mathematical Reasoning Videos 30 videos

CAHSEE Math 1.1 Mathematical Reasoning
228 Views

CAHSEE Mathematical Reasoning: Drill 1, Problem 1. Based on this information, which of the following can be determined?

CAHSEE Math 1.2 Mathematical Reasoning
185 Views

CAHSEE Math Mathematical Reasoning: Drill Set 1, Problem 2. Which of the following should be the most appropriate first step in solving the equation?

CAHSEE Math 1.3 Mathematical Reasoning
183 Views

CAHSEE Math Mathematical Reasoning: Drill 1 Problem 3. Which of the following is the correct order of steps?

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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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