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CAHSEE Math 6.5 Algebra I 202 Views


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Description:

CAHSEE Math: Algebra I Drill 6, Problem 5. How long would it take for Dan and Mike to eat a total of eight slices of pizza?

Language:
English Language

Transcript

00:03

Here’s your shmoop du jour…

00:05

Dan and Mike are brothers, and they’re very competitive.

00:08

Sadly, they don’t have a lick of athletic ability, so the only thing they’re really good at is… eating.

00:13

Dan can eat three slices of pizza in four minutes. Mike can eat six slices in ten minutes.

00:19

To the nearest minute, how long does it take the two of them to eat a total of eight slices of pizza?

00:24

Here are the potential answers…

00:30

So… what is this question asking… other than about the root causes of obesity in America?

00:35

This is a rate, time and distance problem and we have to put things in order and figure

00:39

out how they relate with one another.

00:41

Let’s start by creating a little table…

00:43

Dan: 3 slices in 4 minutes

00:46

Mike: six slices in 10 minutes

00:48

To get the total output – or in this case, er… input… the output will come probably tomorrow.

00:55

…we need to calculate the slices per minute that each consumes.

00:59

So… Dan is at three fourths of a slice per minute and Mike is at six tenths of a slice per minute

01:03

which reduces to three fifths of a slice per minute.

01:07

Now we just have to figure out the time it took them to down 8 slices.

01:11

Cleverly, we’ll call that variable… “t.”

01:15

So the equation we get is 3/4 t plus 3/5 t equals 8.

01:19

Now we just need to solve for t and we’re there.

01:21

We need a common denominator – let’s make it 20, easy enough.

01:25

We multiply top and bottom of the first term by 5 to get 15t over 20.

01:30

Then we’ll multiply top and bottom of the second term by 4 to get 12t over 20… then add ‘em together.

01:36

We get 27t over 20 equals 8.

01:39

Now multiply both sides by 20 to get 27t equals 160.

01:45

Divide both sides by 27 and t equals 160 over 27 which is just about 6 minutes.

01:52

…so the answer is A.

01:53

As in, “Abdominal bloating.”

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