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