Yahoo Answers: Answers and Comments for Find the number of pairs of two numbers whose HCF is 5 and their sum is 50. kindly help!? [Mathematics]
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Wed, 22 May 2019 08:00:41 +0000
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Yahoo Answers: Answers and Comments for Find the number of pairs of two numbers whose HCF is 5 and their sum is 50. kindly help!? [Mathematics]
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From Krishnamurthy: x + y = 50
HCF = 5
5, 45: 15, 35; [35, 15; 4...
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Wed, 22 May 2019 14:39:41 +0000
x + y = 50
HCF = 5
5, 45: 15, 35; [35, 15; 45, 5]

From Ian H: At first we might think of this list
5, 45
10,...
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Wed, 22 May 2019 12:35:51 +0000
At first we might think of this list
5, 45
10, 40
15, 35
20, 30
25, 25
But 10 rather than 5 is the HCF with
10, 40 and
20, 30
and 25, 25 obviously has an HCF of 25,
so that just leaves 5, 45 and 15, 35

From Amy: Both numbers are multiples of 5, so let's ...
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Wed, 22 May 2019 10:53:12 +0000
Both numbers are multiples of 5, so let's call them 5x and 5y.
The constraint is that x and y are positive integers and are relatively prime to each other.
5x + 5y = 50
x + y = 10
List all pairs (x,y) that sum to 10 and meet the stated constraint.

From Dylan: 5a+5b=50
a+b=10 with no common factors
1 and ...
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Wed, 22 May 2019 08:38:03 +0000
5a+5b=50
a+b=10 with no common factors
1 and 9
3 and 7
So....
5 and 45
15 and 35

From Pope: It should take only a moment to check all non...
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Wed, 22 May 2019 08:36:25 +0000
It should take only a moment to check all nonnegative integer pairs that are divisible by five and whose sum is 50. Let the first of the pair increase from zero to 25.
0, 50 ... HCF = 50; reject
5, 45 ... HCF = 5
10, 40 ... HCF = 10; reject
15, 35 ... HCF = 5
20, 30 ... HCF = 10; reject
25, 25 ... HCF = 25; reject
I count two qualifiers.