Answer:
x=24, y=4
Step-by-step explanation:
x=6y
1/x+1/y=7/24,
1/6y+1/y=7/24
1/6y+6/6y=7/24
(1+6)/6y=7/24
7/6y=7/24, then
6y=24
y=24/6
y=4
x=6y=6*4=24
Answer:
The numbers are 4 and 24
Step-by-step explanation:
Let the first number be [tex]x[/tex] and the second number be [tex]y[/tex].
since we were told that one number is 6 times another , let
x = 6y .................................. equation 1
The reciprocal of [tex]x = \frac{1}{x}[/tex]
The reciprocal of [tex]y = \frac{1}{y}[/tex]
The sum of the reciprocal will therefore be :
[tex]\frac{1}{x}+\frac{1}{y}=\frac{7}{24}[/tex] ................................... equation 2
substitute [tex]x = 6y[/tex] into equation 2 , equation 2 then becomes :
[tex]\frac{1}{6y}+\frac{1}{y}=\frac{7}{24}[/tex]
The L.CM is 6y ,
then we have [tex]\frac{1+6}{6y}=\frac{7}{24}[/tex]
[tex]\frac{7}{6y}=\frac{7}{24}[/tex]
since they have the same numerator , we will equate the denominator , that is
[tex]6y = 24[/tex]
divide through by 6
[tex]y = 4[/tex]
substitute [tex]y = 4[/tex] into equation 1 to find the value of x , that is
[tex]x = 6(4)[/tex]
[tex]x = 24[/tex]
Therefore : The numbers are 4 and 24
Check:
[tex]x = 6y[/tex]
[tex]24 = 6(4) = 24[/tex]
[tex]\frac{1}{x}+\frac{1}{y}=\frac{7}{24}[/tex]
[tex]\frac{1}{24}+\frac{1}{4}[/tex]
L.C.M = 24
so we have
[tex]\frac{1+6}{24}[/tex]
= [tex]\frac{7}{24}[/tex]
