one number is four time as large as another number. the sum of thier reciprocal is 1/2. what is the sum of the two numbers?
2007-02-18 01:13:15 · 5 answers · asked by KENT LYROLD G 1 in Science & Mathematics ➔ Mathematics
we have x and 4x
1/x+1/4x=1/2
1/x(1+1/4)=1/2
1/x(5/4)=1/2
x=(5/4)/(1/2)=2.5
so the numbers are
2.5 & 10
and their sum is 12.5
2007-02-18 01:23:45 · answer #1 · answered by Anonymous · 0⤊ 0⤋
First number = x
Second number = 4x
1/x + 1/4x = 1/2
Multiply through by 4x
4 + 1 = 2x
5 = 2x
x = 5/2
So the two numbers are 5/2 and 20/2
The sum of the two numbers is 5/2 + 20/2 = 25/2
2007-02-18 09:18:55 · answer #2 · answered by Tom :: Athier than Thou 6 · 0⤊ 0⤋
First number=4x
Second Number=x
[1/(4x)]+(1/x)=1/2
Multiply 1/4x,1/x and 1/2 by 4x to get a linear equation.
U will get:
1+4=5=2x
When 5=2x
x=5/2.
Multiply it by 4 to get what 4x equals to.
In the end u will get an equation like this:
4x=20/2 (Dont simplify it!)
Add up 5/2 and 20/2 to get the sum.
2007-02-18 10:24:53 · answer #3 · answered by Kenneth Koh 5 · 0⤊ 0⤋
1/x + 1/4x = 1/2
Multiply by 4x
4 +1 = 2x
5=2x
5/2=2
and 10
try it 2/5 + 1/10 = 1/2
2007-02-18 09:25:40 · answer #4 · answered by leo 6 · 0⤊ 0⤋
1. 1/x+1/y = 1/2
2. y = 4x
Substituting #2 into #1 (for y) yields:
1/x+1/(4x)=1/2
4x^2-10x=0
x(4x-10)=0
x=10/4
y=10/4*4 = 10
ANSWER: x=10/4, y=10
2007-02-18 09:23:14 · answer #5 · answered by poor_broke_investor 3 · 0⤊ 0⤋