Two numbers are such that 4 times of the smaller is 5 less than 3 times of the larger, but sum of the numbers is greater than 6 times their difference by 6 . Find the numbers.
Answers
The two numbers are 43 & 59
Given :
Two numbers are such that 4 times of the smaller is 5 less than 3 times of the larger, but sum of the numbers is greater than 6 times their difference by 6
To find :
The two numbers
Solution :
Step 1 of 2 :
Form the equations to find the numbers
Let smaller number = x and larger number = y
Since 4 times of the smaller is 5 less than 3 times of the larger
∴ 4x = 3y - 5
⇒ 4x - 3y = - 5 - - - - - (1)
Again sum of the numbers is greater than 6 times their difference by 6
(x + y) = 6(y - x) + 6
⇒ x + y = 6y - 6x + 6
⇒ 7x - 5y = 6 - - - - - (2)
Step 2 of 2 :
Find the numbers
4x - 3y = - 5 - - - - - (1)
7x - 5y = 6 - - - - - (2)
Multiplying both sides of Equation 1 and Equation 2 by 5 and 3 respectively we get
20x - 15y = - 25 - - - - - (3)
21x - 15y = 18 - - - - - - - (4)
Now Equation 3 - Equation 4 gives
- x = - 43
⇒ x = 43
Putting x = 43 in Equation 1 we get
(4 × 43) - 3y = - 5
⇒ 172 - 3y = - 5
⇒ 3y = 172 + 5
⇒ 3y = 177
⇒ y = 59
So smaller number = 43 & larger number = 59
Hence two numbers are 43 & 59
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