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put this solution on YOUR website!Two positive numbers are in the ratio 3:5. Twice the smaller number exceeds the larger number by 34. Find the numbers.
Let the two positive numbers be a and b. say with a
a and b are in the ratio 3:5
That means a/b = 3/5
That is 5a = 3b ----(1)
Twice the smaller number exceeds the larger number by 34
That is 2a exceeds b by 34
which means (2a-b) = 34 ----(2)
To find a and b
From (2) we have (2a-b) = 34
That is (2a-34) = b ----(*)
Using (*) in (1) we have
5a = 3b giving
5a = 3(2a-34)
5a = 6a - 102
102 = 6a - 5a
102 = a
We have a = 102.
Putting a = 102 in (*)
b= (2a-34) becomes
b = 2X102 - 34 = 204 - 34 = 170
Therefor b = 170
Answer: The two positive numbers are 102 and 170
Verification: Ratio of the two numbers should be 3:5
Therefore a/b = 102/170 = (2X3X17)/(2X5X17) = 3/5 which is correct (cancelling 2X17 in the numerator and in the denominator.)
Twice the smaller number should exceed the larger number by 34
2a should be 34 more than b
That is 2a = 2X102 = 204 should be 34 more than b=170 which is so.
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