Please help, unable to get the right answer after multiple attempts

[ryantzb]

Hi guys, would really appreciate if someone could explain to me how to solve this really simple ratio question.

given that 5w = 2 x and 7x = 3y, find the ratio of w : x : y

Here is my attempt however the answer is wrong.

5W = 2X
7X = 3Y

W : X : Y
5 : 2
.....7 : 3

35:14
.....14: 6

Ans: 35:14:6

 

[Deleted member 4993]

Hi guys, would really appreciate if someone could explain to me how to solve this really simple ratio question.

given that 5w = 2 x and 7x = 3y, find the ratio of w:x:y

Here is my attempt however the answer is wrong.

5W = 2X
7X = 3Y

W : x : Y
5 : 2
7 : 3

35:14
14: 6

Ans: 35:14:6

5*w = 2*x ..............................(1)

3*y = 7*x ..............................(2)

If you divide (1) by (2), we get:

(5*w)/(3*y) = (2*x)/(7*x)

Now simplify and continue....

 

[ryantzb]

5*w = 2*x ..............................(1)

3*y = 7*x ..............................(2)

If you divide (1) by (2), we get:

(5*w)/(3*y) = (2*x)/(7*x)

Now simplify and continue....

Thanks so much for helping, however, as I am quite a slow learner, if you are free, do you mind explaining a little more as I am really confused. Thanks so much for your time

 

[stapel]

...as I am quite a slow learner, if you are free, do you mind explaining a little more as I am really confused.

Kindly please reply with specification regarding where the explanation stopped making sense for you. Thank you!

 

[stapel]

...however the answer is wrong.

What have you been given as being the expected ("right") answer? Thank you!

 

[Ishuda]

Hi guys, would really appreciate if someone could explain to me how to solve this really simple ratio question.

given that 5w = 2 x and 7x = 3y, find the ratio of w : x : y

Here is my attempt however the answer is wrong.

5W = 2X
7X = 3Y

W : X : Y
5 : 2
.....7 : 3

35:14
.....14: 6

Ans: 35:14:6

If yours is wrong, what is the given answer?

 

[Ishuda]

Given answer is 35-14-6.
He's saying (unclearly) that he can't get the given answer.

Now I'm confused, ryantzb said

Here is my attempt however the answer is wrong.

5W = 2X
7X = 3Y

W : X : Y
5 : 2
.....7 : 3

35:14
.....14: 6

What ryantzb has done [multiply the first W:X:Y row by 7 and the second row by 2] is certainly one way to go about solving the problem. In fact, I think I might find it easier than
W=(2/5) X = (2/5) (3/7) Y
and multiply through by 35 to get
35 W = 14 X = 6 Y implies ratios for W:X:Y of 35:14:6

 

[ryantzb]

What ryantzb has done [multiply the first W:X:Y row by 7 and the second row by 2] is certainly one way to go about solving the problem. In fact, I think I might find it easier than
W=(2/5) X = (2/5) (3/7) Y
and multiply through by 35 to get
35 W = 14 X = 6 Y implies ratios for W:X:Y of 35:14:6

Yeah, thats what I did

Given answer is 35-14-6.
He's saying (unclearly) that he can't get the given answer.

Im sorry if I did not phrase it well enough, what im trying to say is that 35-14-6 is the answer that I derived at however, it is not correct when I checked the answer key

What have you been given as being the expected ("right") answer? Thank you! :wink:

If yours is wrong, what is the given answer?

The right answer from the answer key would be

W : X : Y
6 :15: 35

Kindly please reply with specification regarding where the explanation stopped making sense for you. Thank you! :wink:

What I do not understand is how I can derive at 6 - 15 - 35 (correct answer),
with the clues given

5*w = 2*x ..............................(1)

3*y = 7*x ..............................(2)

If you divide (1) by (2), we get:

(5*w)/(3*y) = (2*x)/(7*x)

Now simplify and continue....

Hint: if a/x = b/y then b = ay/x

 

[Deleted member 4993]

hi guys, would really appreciate if someone could explain to me how to solve this really simple ratio question.

Given that 5w = 2 x and 7x = 3y, find the ratio of w : X : Y

here is my attempt however the answer is wrong.

5w = 2x
7x = 3y

w : x : Y
5 : 2
.....7 : 3

35:14
.....14: 6

ans: 35:14:6

w : x

2 : 5 → 6 : 15

.....x : y

.....3 : 7 → 15 : 35

w : x : y → 6 : 15 : 35

 

[Ishuda]

...
What ryantzb has done [multiply the first W:X:Y row by 7 and the second row by 2]...

Yeah, thats what I did ...

And fell into the same trap I did. If W:X as a:b then bW=aX so both of us got it backwards. In this case 5W=2X so b=5 and a=2, i.e. (as Subhotosh Khan posted)
W:X:Y
2 :5
__7:3
So now multiply the first row by 7 and the second row by 5.

Hey Denise, you still there in the corner. I'll join you so we can both have some company.

 

[ryantzb]

w : x

2 : 5 → 6 : 15

.....x : y

.....3 : 7 → 15 : 35

w : x : y → 6 : 15 : 35

Thanks so much for this, was planning to give up when I first saw you posting that the answer key is wrong as I was quite sure the answer key is correct. Thanks again

And fell into the same trap I did. If W:X as a:b then bW=aX so both of us got it backwards. In this case 5W=2X so b=5 and a=2, i.e. (as Subhotosh Khan posted)
W:X:Y
2 :5
__7:3
So now multiply the first row by 7 and the second row by 5.

Hey Denise, you still there in the corner. I'll join you so we can both have some company.

Thanks so much for the explanation, really appreciate it. However, even though I know this is the way, I just do not understand why 5W = 2X should be interpreted as 2 - 5. Of course since this is the way to do it I will just memorize it but is there like a way to explain this? Thanks so much for you time

 

[Ishuda]

...However, even though I know this is the way, I just do not understand why 5W = 2X should be interpreted as 2 - 5. Of course since this is the way to do it I will just memorize it but is there like a way to explain this? Thanks so much for you time

It's that sneaky thing about being in the denominator. That is ratios (proportions) are expressed as fractions:
\(\displaystyle W:X=\frac{W}{X}\)
so
\(\displaystyle W:X=A:B\)
means
\(\displaystyle \frac{W}{X}\, =\, \frac{A}{B}\)
or
B W = A X

It's something like the same type of trap some people fall into when, for example, computing an average speed: You go 25 mph for 1 hr and 40 mph for 1/2 hr. What is the average speed? Well, if we average the 25 and 40 we get 32.5 mph which is wrong. That's because the time variable occurs in the denominator, i.e. mph = distance/time = 45 / 1.5 = 30.

 

[ryantzb]

It's that sneaky thing about being in the denominator. That is ratios (proportions) are expressed as fractions:
\(\displaystyle W:X=\frac{W}{X}\)
so
\(\displaystyle W:X=A:B\)
means
\(\displaystyle \frac{W}{X}\, =\, \frac{A}{B}\)
or
B W = A X

It's something like the same type of trap some people fall into when, for example, computing an average speed: You go 25 mph for 1 hr and 40 mph for 1/2 hr. What is the average speed? Well, if we average the 25 and 40 we get 32.5 mph which is wrong. That's because the time variable occurs in the denominator, i.e. mph = distance/time = 45 / 1.5 = 30.

Omg, thanks so so so so much! I finally got it, Thank you thank you thank you. I really appreciate it! ,I understand fully now. Once again thank you so so much!