The number of pairs of integers \((x , y)\) satisfying \(x≥y≥-20\) and \(2x+5y=99\) is
[This Question was asked as TITA]
[This Question was asked as TITA]
- 18
- 11
- 15
- 17
The Correct Option is D
Solution and Explanation
\(2x+5y=99\)
When, \(y=-19,\ x=97\);since \(x≥y;\) the maximum value of y is \(13\)and corresponding value of x is \(17\).
We know that the solutions of y are in arithmetic progression with common difference \(2\).
Here, \(a=-19,\ d=2,\ t_n=13\)
\(t_n=a+(n-1)d\)
\(-19+(n-1)(2)=13\)
\((n-1)2=32\)
\(⇒ n=17\)
Hence number of pairs integers is \(17\)
So, the correct option is (D): \(17\)
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