If 2x + 3y = 50 and x, y ∈ N, then what is the value of x for which y is minimum?
Show answer & explanation
Correct answer: B
Explanation
Given:
2x + 3y = 50, where x, y ∈ N
y = (50 − 2x)/3
For y to be minimum, x must be maximum, and (50 − 2x) must be divisible by 3.
50 − 2x ≡ 0 (mod 3)
2x ≡ 2 (mod 3)
x ≡ 1 (mod 3)
The largest natural value less than 50 satisfying x ≡ 1 (mod 3) is 22.
Check:
2(22) + 3(2) = 44 + 6 = 50
Thus, y = 2 (minimum)
Answer: x = 22