Examples on Numbers 3
In this class, We discuss Examples on Numbers 3.
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Example 1:
Fifty is divided into two parts the sum of their reciprocals is 1/12. Find the two parts.
Solution:
We do not know the values of each part, so we take it as x.
Two parts are x, 50-x.
1/x + 1/(50-x) = 1/12
((50 – x) + x)/(x(50-x)) = 1/12
x^2 – 50x + 600 = 0
(x-30)(x-20) = 0
x = 30 or x = 20
parts are 30,20.
Example 2:
If three numbers are added in pairs, the sums equal 10, 19, and 21. Find the numbers?
Solution:
Let numbers be x, y, and z.
x+y = 10
y+z = 19
x+z = 21
Add above three equations we get 2(x+y+z) = 50
x+y+z = 25.
x = 25 – 19 = 6
y = 25 – 21 = 4
z = 25 – 10 = 15