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