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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Ashley (Customer)

[00:00:01] The length of a Charlotte, North Carolina, conservatory garden is 20 yards greater than its width. The area is 300 square yards. What are the dimensions?

John A (Tutor)

[00:00:07] Welcome to Tutor.com ! My name is John

[00:00:11] How are you doing today?

Ashley (Customer)

[00:00:13] Hi! :)

[00:00:16] I'm doing great, how about you?

John A (Tutor)

[00:00:28] Great, thanks for asking!

[00:00:34] Is this your first time using Tutor.com ?

Ashley (Customer)

[00:00:33] No problem :)

[00:00:41] Nope!

John A (Tutor)

[00:01:02] Ok good to have you back.
So, do you have some ideas about this one?

Ashley (Customer)

[00:01:19] No..

John A (Tutor)

[00:01:36] That's ok, let's take a look.
Have you been using equations in class?

Ashley (Customer)

[00:01:44] Yes.

John A (Tutor)

[00:02:05] Ok awesome.
It's going to be a little tricky, but I think we can make an equation for this one

[00:02:10] First

[00:02:14] what shape is the garden?

Ashley (Customer)

[00:02:23] I think it's a rectangle

John A (Tutor)

[00:02:41] I think so too; I like to draw pictures for these, it really helps

[00:02:48] And we'll mark the length and width

[00:03:05] How does that look so far?

Ashley (Customer)

[00:03:12] Great(:

John A (Tutor)

[00:03:21] Awesome

[00:03:43] Whenever we don't know what something is in math....we can use a "variable," like x

Ashley (Customer)

[00:03:50] Since we're going to use an equation I was guessing that we should use x for width and (x + 20) for its length and make it equal to 300 like x + (x + 20) = 300

John A (Tutor)

[00:03:57] It's "variable" because we don't know what it is!

[00:04:13] That's really close!!!

[00:04:19] The only thing you're missing is

[00:04:27] how do we calculate the area of a rectangle?

Ashley (Customer)

[00:04:37] length x width

John A (Tutor)

[00:04:49] Right, we multiply

[00:04:55] did you multiply in your equation?

[00:04:59] length x width

Ashley (Customer)

[00:04:58] nop

[00:05:00] Nope*

[00:05:01] I added

John A (Tutor)

[00:05:06] Exactly

[00:05:13] What would it be if we multiplied?

Ashley (Customer)

[00:05:22] x(x + 20) = 300

John A (Tutor)

[00:05:30] Yep! Nice job

[00:05:49] Now we need to solve that equation...hmm, any ideas?

Ashley (Customer)

[00:06:14] We should probably distribute the x on the left side first

John A (Tutor)

[00:06:21] Good idea

[00:06:25] What will that give us?

Ashley (Customer)

[00:06:34] x^2 + 20x

John A (Tutor)

[00:06:51] Now what?

Ashley (Customer)

[00:07:08] Subtract the 300 from both sides.?

John A (Tutor)

[00:07:18] Exactly right

[00:07:22] And what do we get?

Ashley (Customer)

[00:07:37] x^2 + 20x - 300 = 0

John A (Tutor)

[00:08:01] Ok great, any ideas on what we should try next

Ashley (Customer)

[00:08:23] No.

John A (Tutor)

[00:08:34] Do you remember factoring from class?

Ashley (Customer)

[00:08:50] Yes, that's what I was thinking of doing but I wasn't sure.

John A (Tutor)

[00:09:19] Yeah, we could factor, or we could use the quadratic formula.
Either way is going to be a little tough

[00:09:26] Let's try factoring

Ashley (Customer)

[00:09:47] Ok.

John A (Tutor)

[00:10:04] To factor we want to think of two things

[00:10:12] First, we want to find factors of 300

[00:10:21] and second, we want those factors to add up to 20

[00:10:30] Can you think of some factors of 300?

Ashley (Customer)

[00:11:07] 2, 10, 20

John A (Tutor)

[00:11:15] Perfect

Ashley (Customer)

[00:11:21] 4

John A (Tutor)

[00:11:36] Let's look at 2 first

[00:11:46] What do we need to multiply 2 by to get -300?

Ashley (Customer)

[00:11:52] -150

[00:12:00] That definitely won't add up to 20

John A (Tutor)

[00:12:08] Right, definitely not

[00:12:15] probably need a bigger number than 2

[00:12:25] Ideas?

Ashley (Customer)

[00:12:35] I know 4 won't work.

John A (Tutor)

[00:12:46] No, that would still be too small

Ashley (Customer)

[00:12:58] 10?

John A (Tutor)

[00:13:00] What about 10?

[00:13:11] Yeah, what do we need to multiply 10 by to get -300?

Ashley (Customer)

[00:13:18] -30

[00:13:24] And -30 + 10 = 20

[00:13:27] So that works :)

John A (Tutor)

[00:13:33] Close......

[00:13:36] -30 + 10 = -20

[00:13:49] we need positive 20

Ashley (Customer)

[00:13:57] So -10 + 30

John A (Tutor)

[00:14:07] Right! So we use those

[00:14:37] and put them in our factors like that

[00:14:44] Now the last step is we solve

[00:14:57] Do you remember how to get the solutions for that?

Ashley (Customer)

[00:15:02] Yes.

[00:15:08] x = 10 and x = -30

John A (Tutor)

[00:15:21] Nice job!

[00:15:28] Hmmm, which one of those could be a length?

Ashley (Customer)

[00:15:33] 10!

John A (Tutor)

[00:15:48] And that's our answer! 10

[00:15:55] What was x though?

Ashley (Customer)

[00:15:55] Yay! :)

John A (Tutor)

[00:16:22] Was x the area of our rectangle?

Ashley (Customer)

[00:16:20] Width

John A (Tutor)

[00:16:26] Right

[00:16:30] So our width = 10

[00:16:34] What is our length?

Ashley (Customer)

[00:16:33] No

[00:16:38] 30

John A (Tutor)

[00:16:59] And we're done!!! Nice work

Ashley (Customer)

[00:17:14] Thank you so much for your help! :)

John A (Tutor)

[00:17:20] Do you have any questions about this one before we close up?

[00:17:26] No problem :)

Ashley (Customer)

[00:17:24] Nope!

John A (Tutor)

[00:17:31] Ok, have a good day

Ashley (Customer)

[00:17:31] Have a great evening(:

John A (Tutor)

[00:17:36] Thanks for using Tutor.com, please fill out the survey, it's really helpful

[00:17:37] thanks!

Ashley (Customer)

[00:17:38] Thanks!

[00:17:41] I will(:

[00:17:41] Bye!

John A (Tutor)

[00:17:50] bye!