Examples on Numbers 4

In this class, We discuss Examples on Numbers 4.

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Example 1:

The sum of the three numbers is 136. the ratio between the first and second is 2:3, and that between the second and third is 5 : 3.

The second number is?

Solution:

Let the numbers be A, B, and C.

A : B= 2: 3

B : C = 5 : 3

Multiply both sides with 3/5 we get (3/5 * 5): (3/5 * 3)

= 3 : 9/5

Multiplying both sides with the same number will not change the ratio.

A : B = 2 : 3

B : C = 3 : 9/5

We can combine as A: B: C because B is the same value.

A : B : C = 2 : 3 : 9/5

= 10 : 15 : 9

The second number is 136 * 15/34

= 60

Example 2:

If the fraction’s numerator increased by two and the denominator increased by three, the fraction becomes 7/9.

If the numerator and denominator decreased by one, the fraction became 4/5.

What is the original fraction?

Solution:

Let the fraction is x/y

(x+2)/(y+3) = 7/9

(x-1)/(y-1) = 4/5

The equations we get are

9x – 7y = 3

5x – 4y = 1

Solving the equations we get x = 5 and y = 6

The fraction is x/y = 5/6