Answer:
10 and 15
Step-by-step explanation:
Let 'x' and 'y' are the numbers we need to find.
x + y = 25 (two numbers whose sum is 25)
(1/x) + (1/y) = 1/6 (the sum of whose reciprocals is 1/6)
The solutions of the this system of equations are the numbers we need to find.
x = 25 - y
1/(25 - y) + 1/y = 1/6 multiply both sides by 6(25-y)y
6y + 6(25-y) = (25-y)y
6y + 150 - 6y = 25y - (y^2)
y^2 - 25y + 150 = 0 quadratic equation has 2 solutions
y1 = 15
y2 = 10
Thus we have
:
First solution: for y = 15, x = 25 - 15 = 10
Second solution: for y = 10, x = 25 - 10 = 15
The first and the second solution are in fact the same one solution we are looking for: the two numbers are 10 and 15 (since the combination 10 and 15 is the same as 15 and 10).
Answer:
12
Step-by-step explanation:
Answer:
Let the original number be x
Successor is defined as the number which comes immediately after a particular number.
also, the successor of a whole number is the number obtained by adding 1 to that number.
Then, the successor of a number x is, x+1
As per the given condition :
we have;
Using distributive property on LHS (i.e, 
)
Then, we have
5x+5+x=83
Combine like terms;
6x+5=83
Subtract 5 from both the sides we get;
6x+5-5=83-5
Simplify:
6x=78
Divide both side by 6,
Simplify:
x =13
Therefore, the original number x is, 13
I'm working on the same thing down load the algebra tiger it really helps a lot I promise I use it daily to help with these
