Question

A 30in board is cut into 3 pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.

Answer 1

30in = stuff

Answer 2

1st piece will just be x
2nd ?
3rd?

What do you think?

Answer 3

y and z?

Answer 4

we don't need y and z. The x represents a dimension or a length.

Answer 5

I'm sorry. So, then what do you mean with "What do you think?"

Answer 6

Hello.

Answer 7

Hello!

Answer 8

Look at the relation stated in the passage: 4 times and 5 times of the x value.

Answer 9

30 inches as a whole.

Answer 10

Understood so far.

Answer 11

I took a random value, for x, x = 3. 4(3) = 12. 5(3) = 15.
3 + 12 + 15 = 30. Amazingly, this is the correct value. I have always had a unique ability to guess the value quite quickly.

Answer 12

3 pieces, added all together equals the whole.

Answer 13

9x + 3 = 30.

Answer 14

9x = 27 x = 3. For Algebra stance.

Answer 15

Then just plug in 3 for 4(x) and 5(x) and see if it adds up to 30, which it does.

Answer 16

x = inches

Answer 17

I apologize, raffle. I had to share when I found the answer on my first guess, haha.

Answer 18

4 times, means 4 times greater than x amount.

Answer 19

No worries, more help the better as long as OP is learning I am fine.

Answer 20

Kpop, understand everything we said? Need any further explanation?

Answer 21

Wait, did you randomly just choose 3? Because, what I'm more confused about is trying to make it into an equation then solving for x.

Answer 22

Yes, I randomly choice 3, myself, but when I looked at the problem further I see that there is 4x and 5x and 3 pieces. So I constructed a equation like this: 9x + 3 = 30 (the total inches)

Answer 23

Then solved for x.

Answer 24

There's always more than one way to solve a puzzle.

Answer 25

Would you know how to put it into an equation without guessing numbers? Is there a formula I can use?

Answer 26

I didn't use a formula, more so, I looked at what the passage gave me. The equation I made wasn't a guess. 4x + 5x + 3 = 30. All from the passage.

Answer 27

i meant without guessing a number

Answer 28

9x + 3 = 30
9x = 27
x = 3
3 + 4(3) + 5(3)
3 + 12 + 15 = 30
30 = 30.

Answer 29

I never guessed a number in what I just stated.

Answer 30

All this information came from what you stated.

Answer 31

Oh!! Because of the three pieces, right?

Answer 32

Yes.

Answer 33

I only combined like-terms with the 4x and 5x, also.

Answer 34

So, for example if it was cut into 5 pieces, I can use the number 5 just like what you did with 3?

Answer 35

If need be, then I would hope so, because that's how I saw it, and it worked out just fine. So, the chances of that happening has a good value, but it doesn't mean it will work every time.

Answer 36

Let's see, I will make an example:

Answer 37

75 = 5 + 14x
(x) + 2x + 3x + 4x + 5x

Answer 38

For 5 pieces.

Answer 39

70 = 14x
x = 5

Answer 40

So, it does work in that case also. So, it seems to work in more than one case.

Answer 41

5 + 10 + 15 + 20 + 25 = 75, by the way.

Answer 42

1(5) + 2(5) + 3(5) + 4(5) + 5(5) = 75.

Answer 43

Oh, okay. I think this is much easier than how I tried learning it in class. It was more detailed in class.

Answer 44

Always remember there is more than one way to solve a puzzle, no matter the difficulty. (:

Answer 45

Haha, I will. Thanks so much. I really appreciate you helping me out.

Answer 46

Anytime, medal if you wish. You have a goodnight/good day! (:

Answer 47

Of course. Thank you. You too :)