there are two positive numbers such that the sum of twice the first number and thrice the second number is 39 while the sum of thrice the first and twice the second is 36 ( the linear equation of this question only need)
Answers
Step-by-step explanation:
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Question :
There are two positive numbers such that the sum of twice the first number and thrice the second number is 39 while the sum of thrice the first and twice the second is 36. Find the numbers.
Answer :
The first number is 6 and the second number is 9.
Given :
The sum of twice the first number and thrice the second number = 39
The sum of thrice the first and twice the second = 36
To find :
The two positive numbers
Solution :
Let the first number be x
and the second number be y
According to the first problem ,
2x + 3y = 39........i
According to the second problem ,
3x + 2y = 36........ii
Isolating x from equation i ,
2x + 3y = 39
=> 2x = 39 - 3y
=> x = ( 39 - 3y ) / 2
Putting the value of x in equation ii ,
3x + 2y = 36
=> 3 ((39 - 3y)/2) + 2y = 36
=> (117 - 9y)/2 + 2y = 36
=> 117 - 9y + 4y = 72
=> 117 - 5y = 72
=> 117 - 72 = 5y
=> 45 = 5y
y = 45/5
= 9
Putting the value of y in equation i ,
2x + 3y = 39
=> 2x + 3 × 9 = 39
=> 2x + 27 = 39
=> 2x = 39 - 27
=> 2x = 12
=> x = 12/2
= 6
Hence, the first number is 6 and the second number is 9.
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