The sum of two numbers is 15 ,if the sum of their reciprocal s is 3/10,find the numbers?

Question

Answer

Let the numbers be x and y ,
sum of numbers =15,
x+y=15,--(1)
and 1/x+1/y=3/10,
x+y/xy=3/10,
from (1).
15/xy=3/10,
xy=50--(2).
from (1). x=15-y ,
put x=15-y in (2).
(15-y)y=50,
15y-y^2=50,
y^2-15y+50=0,
by splitting the middle term,
y^2-10y-5y+50=0,
y(y-10)-5(y-10)=0,
y-10=0, or, y-5=0,
y=10, or ,y=5,
Case 1.put y=10 in (1).
x+10=15,
x=5 ,
Case 2.put y=5 in (1).
x+5=15,
x=10,
so, x=5 or, 10

Answer

10 and 5

Answer

Let the no.s be x and 15-x 1/x +1/15-x=3/10 15/x(15-x)=3/10 150=45x-3x^2 3x^2-45x +150=0 x^2-15x+ 50=0 ×=10,5

Answer

Problem Statement: The sum of two numbers is 15. If the sum of their reciprocals is 3/10, find the numbers.

Solution:

Let's assume the two numbers as x and y.

Given:
x + y = 15
1/x + 1/y = 3/10

To find the values of x and y, we can follow the steps below:

Step 1: Simplify the second equation:
Multiply both sides of the second equation by xy to eliminate the denominators:
xy * (1/x) + xy * (1/y) = (3/10) * xy
y + x = (3/10) * xy

Step 2: Express one variable in terms of the other:
Rearrange the first equation to express y in terms of x:
y = 15 - x

Step 3: Substitute the value of y in the second equation:
Substitute (15 - x) for y in the equation y + x = (3/10) * xy:
(15 - x) + x = (3/10) * x(15 - x)

Step 4: Simplify and solve for x:
15 - x + x = (3/10) * (15x - x^2)
15 = (3/10) * (15x - x^2)
150 = 3(15x - x^2)
50 = 15x - x^2
x^2 - 15x + 50 = 0

Step 5: Solve the quadratic equation:
Factor the quadratic equation or solve it using the quadratic formula to find the values of x.

x^2 - 15x + 50 = 0
(x - 10)(x - 5) = 0

So, the possible values for x are x = 10 and x = 5.

Step 6: Find the corresponding values of y:
Using the equation y = 15 - x, substitute the values of x to find the corresponding values of y.

For x = 10, y = 15 - 10 = 5
For x = 5, y = 15 - 5 = 10

Therefore, the two numbers are 10 and 5.

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