Question

three positive number are in the ratio 1/2:1/3:1/4 .Find the numbers if the sum of their squares is 244
@perl

Answer 1

Ratios are"
\[\frac{ 1 }{ 2 }:\frac{ 1 }{ 3 }:\frac{ 1 }{ 4 }\]

Answer 2

\[244\]
Is the sum of THEIR squares.

Answer 3

@perl

Answer 4

Hints:
1. sum of squares form an integer, there is a good chance the numbers are integers.
2. numbers are in ratios 1/2:1/3:1/4. The LCM of 2,3,4 is 12.
3. So the numbers are in the ratio 12/2:12/3:12/4=6:4:3.
4. sum of squares of 6,4,3=36+16+9=61 = 244/4.
5. Will let you figure out the rest of the problem.

Answer 5

???

Answer 6

@mathmate

Answer 7

In math, we do a lot of trial and error, and the deductions made when we get the right (or wrong) answer is the thinking process required in learning math.
So I strongly suggest you do some number work to get the answer, or post your tries so we can take it from there.

Answer 8

See if you can eliminate y and z, so you have one equation in one variable

Answer 9

???

Answer 10

\(\color{blue}{\text{Originally Posted by}}\) @AaronAndyson
???
\(\color{blue}{\text{End of Quote}}\)

Can you be more specific

Answer 11

I did not understand what you me to do...

Answer 12

What next @perl?

Answer 13

@welshfella

Answer 14

x^2 + y^2 + z^2 = 244

x: y : z = 1/2 : 1/3 : 1/4

multiply ratio through by LCM of 2,3,4 which is 12
1/2 : 1/3 : 1/4 ⟺ 12*1/2 : 12* 1/3 : 12 * 1/4 = 6 : 4: 3

So far we have
x^2 + y^2 + z^2 = 244
x: y : z = 6 : 4: 3

Now lets look at the ratio more closely
The ratio gives us three equation:

x/y = 6/4 -> 4x = 6y
x/z = 6/3 -> 3x = 6z
y/z = 4/3 -> 3y = 4z

Answer 15

Our goal is to produce one equation in one unknown. We have derived the following equations:

x^2 + y^2 + z^2 = 244
4x = 6y
3x = 6z
3y = 4z

y = 4/3 z
x = 6/3 z = 2z

so lets substitute these

(2z)^2 + (4/3)^2 + z^2 = 244

now we have one equation in one unknown

Answer 16

???

Answer 17

i DIDN'T UNDERSTAND :(

Answer 18

what level of math are you, i hope this isn't too advanced

Answer 19

Sophomore in high school
Doing this chapter after like MONTHS

Answer 20

ok can you point to the line which does not make sense,

Answer 21

The equation you formed...

Answer 22

\(\color{blue}{\text{Originally Posted by}}\) @perl
x^2 + y^2 + z^2 = 244

x: y : z = 1/2 : 1/3 : 1/4

multiply ratio through by LCM of 2,3,4 which is 12
1/2 : 1/3 : 1/4 ⟺ 12*1/2 : 12* 1/3 : 12 * 1/4 = 6 : 4: 3

So far we have
x^2 + y^2 + z^2 = 244
x: y : z = 6 : 4: 3

Now lets look at the ratio more closely
The ratio gives us three equation:

x/y = 6/4 -> 4x = 6y
x/z = 6/3 -> 3x = 6z
y/z = 4/3 -> 3y = 4z
\(\color{blue}{\text{End of Quote}}\)

Does this make sense so far?

Answer 23

Yes.