How many pairs of positive integers (a, b), where a b, satisfy 2a +

Question

How many pairs of positive integers (a, b), where a > b, satisfy 2a + 5b = 103?

A. 6
B. 7
C. 8
D. 9
E. 14

firas92 · Accepted Answer

Since a and b are integers, 2a is even and so 5b must be odd which means b is odd.

If a=b, 7b=103, b=14.xxx

Since a>b, b can take any odd value from 1 to 14.

That is b=1,3,5,7,9,11 or 13 = 7 values

Answer is (B)

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LevMik · Answer

there are 7 pairs 
In order a to be integer diff 103-5b must be divided by 2, so b is odd
If a>b then 
49 :1/ 3:44/ 5:39 ... 13:19

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ankitgoswami · Answer

2a + 5b = 103

so 2a and 5b will add up to give 3 at unit's place only if they have 5 and 8 at unit's place like in this case, they are of the order 8,95 or 18,85 or 28,75 or.....

so possible cases here are (8,95), (18,85), (28,75), (38,65), (48,55), (58,45), (68,35), (78,25), (88,15), (98,5).

So likely a and b becomes (4,19), (9,17), (14,15), (19,13), (24,11), (29,9), (34,7), (39,5), (44,3), (49,1).

Now it's given that a>b.

So we are left with (19,13), (24,11), (29,9), (34,7), (39,5), (44,3), (49,1).

A total of 7 pairs.

Ans =  B .

Kinshook · Answer

Asked: How many pairs of positive integers (a, b), where a > b, satisfy 2a + 5b = 103?

(a, b) = (49,1) satisfy the equation.
(a, b) = {(49,1),(44,3),(39,5),(34,7),(29,9),(24,11),(19,13)}: 7 pairs

IMO B

Kinshook · Answer

Asked: How many pairs of positive integers (a, b), where a > b, satisfy 2a + 5b = 103?

b = (103-2a)/5
When a = 4; b = 19

(a, b) = {(4,19), (9,17), (14,15), (19, 13), (24, 11), (29, 9), (34, 7), (39, 5), (44, 3), (49, 1)} 
Since a> b

(a , b) = {(19, 13), (24, 11), (29, 9), (34, 7), (39, 5), (44, 3), (49, 1)} : 7 pairs

IMO B

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How many pairs of positive integers (a, b), where a > b, satisfy 2a +

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