Question

The ratio of two numbers is 5:7. If 6 is added to each number, the ratio of the numbers is 7:9. What are the numbers?

Answer 1

difference between the numbers is 2.
6/2 = 3

3 x 5 = 15 3 x 7 = 21

numbers are 15 and 21

Answer 2

How did you find the difference of the numbers equals 2???

Answer 3

5 : 7
+2 +2
7 : 9

Answer 4

I get that,but 6 is added to each not 2???

Answer 5

yes but these are scaled down so we need to find how much they are scaled down to, by finding the ratio to the two ratios we can find that they are scaled down by 3.

Answer 6

I'm sorry,but I don't quit understand.

Answer 7

I know its hard to explain over chat... hmm.. how can I put this.

Answer 8

The part I don't understand is the scaled down part.

Answer 9

alright well we know that the numbers are not 5 and 7, these are just simplified versions of the real numbers.

Answer 10

ok

Answer 11

so that means that 5:7 to 7:9 just adds 2 to both the numbers, not 6 lie the problem says. so how do we get from 2 to 6?

Answer 12

I'm lost on how to get from 2 to 6.

Answer 13

we always multiply when we are talking ratios..

Answer 14

2 x 3 = 6

Answer 15

so 3 is our scale for the whole entire equation

Answer 16

lets multiply all our numbers by our scale

5:7
7:9

15:21
21:28

Answer 17

What do you mean by scale? i guess i haven't learned this term yet

Answer 18

Usually I work these problems by cross multiplying if that is any help.

Answer 19

Ill find out how to explain this indeed! :)

Answer 20

these are simplified ratios. which means that they were simplified with one single number correct?

Answer 21

Yes

Answer 22

we are trying to find that one number. we are given that between the two numbers, 6 is added, but since it is scaled down, so is that 6.

Answer 23

hold on... this might take a minute for me to understand.

Answer 24

its ok :)

Answer 25

i am sorry. i am lost again

Answer 26

example:

3:6 + 6 = 9:12

Answer 27

ok doky

Answer 28

this WHOLE equation can be simplified by one number.. do you know what that number is?

Answer 29

6??? or 2???

Answer 30

one number that goes into 3, 6, 9 and 12

Answer 31

what???

Answer 32

3 goes into all those numbers

Answer 33

so we simplify our equation and divide 3 by all the numbers.

1:3 + 2 = 3:4

Confused there?

Answer 34

Oh duuu!!! I am sorry my brain isn't cooperating right now.:)

Answer 35

lol its all good :) so the number that we added to the first ratio changed from 6 to 2. We are trying to work this backwards, this is what we have.

5:7 + 2 = 7:9

x:x + 6 = x:x

what number can we mulitpy everything by to get the top equation to look like the bottom?

Answer 36

ignoring the x's and focusing on the number we do have, 6

Answer 37

not trying to get the answer out of you or anything I just learned this concept today so i'm really not as stupid as i seem:)

Answer 38

give me 1 sec...

Answer 39

hey its all good I understand! we use multiplication, which means solve this

2 * x = 6

Answer 40

or x = 6/2

Answer 41

x=3?

Answer 42

YES you got it! so we take that 3 and we multiply it by the rest of the equation

5 : 7 + 2 = 7 : 9
x3 x3 x3 x3 x3

15:21 + 6 = 21:28

notice how the 6 is in the same place it was like this one:

5:7 + 2 = 7:9

x:x + 6 = x:x

and 15 + 6 = 21
21 + 6 = 28

Everything checks out!

Answer 43

Just one question isn't the 9 times the 3x actually 27???

Answer 44

and 21 +6 = 27

Answer 45

yup sorry lol

Answer 46

Thanks so much for sticking with me and I was wondering if you could help with a couple more???
I knew it was 27 just messing with you:)

Answer 47

No problem Boyce! and sure I could help you with a couple more

Answer 48

Thanks, your awesome!! just give me one sec to transfer my answer.:)

Answer 49

No problem!

Answer 50

Ok here is another... The ratio of the length to the width of a rectangle field is 5:4. The perimeter of the field is 324 meters. What are the dimensions?

Answer 51

P=2l+2w

Answer 52

thats the perimeter equation

Answer 53

You got it.:)

Answer 54

the perimeter is 324 i just don't get how to get the dimensions

Answer 55

so it just gives you the perimeter and thats it? no pics or anything?

Answer 56

All is gives is that little hint that P=2L +2w

Answer 57

there has to be more information...

Answer 58

I know I don't know what to tell you. I am confused too.

Answer 59

i don't know how it is even possible to get an answer from that

Answer 60

it could be anything from l = 100 w = 62 to l = 50 w = 112

Answer 61

is it multiple choice?

Answer 62

no, but give me one second I am going to look at my booklet

Answer 63

ok

Answer 64

maybe L=5x and w=4x do you think that is possible???

Answer 65

why the x's?

Answer 66

Cause then There is the formula A=lw that I found in the booklet. so Then i could substitute the L=5x and the w=4x

Answer 67

does it give you area?

Answer 68

no, but just give me a sec I may have it:)

Answer 69

ok sweet :)

Answer 70

Yes I got it do you want to see???

Answer 71

YESSS lol

Answer 72

Ok I have to take in this moment it makes me feel so smart:) R u ready??? lol

Answer 73

DO IT!! hahaha

Answer 74

So l=5x and w=4x

And keep in mend that P=2L +2w

324=2[5x] +2[4x]

324=10x +8x

324=18x

18=x or x=18

The numbers are 5x and 4x so they are:

5(18)=90

4(18)=72

BOOM!!! lol

Answer 75

look at you!!!! nice!!!

Answer 76

Can i do another problem with you that is if i don't figure it out first.he he he???

Answer 77

hahahaha sure!

Answer 78

ok doky

Answer 79

Here is another... a^2-25/a+5=6/3 i need to solve by cross multiplying

Answer 80

I keep getting 35 for my answer but it won't check

Answer 81

could you start a new question and mention me in it the more comments we put in the slower my computer gets...

Answer 82

me too sure