If 5a + 7b = k, where a and b are positive integers, what is the largest possible value of k for which exactly one pair of integers (a, b) makes the equation true?  Choose the correct choice
A) 35 B) 48 C) 69 D) 70 E) 74
We 'll start putting the values of with a = 10 and b = 1.   Keep decreasing the value of a by 1 and increasing the value of b by 1.   At a = 10 and b = 1, 5a + 7b = 57   At a = 9 and b = 2, 5a + 7b = 59   At a = 8 and b = 3, 5a + 7b = 61   We see a pattern, for every decrease in a and every decrease in b, the result is increasing by 2.   So,   At a = 4 and b = 7, 5a + 7b = 69.   ANSWER:69
<result>C</result>
If 5a + 7b = k, where a and b are positive integers, what is the largest possible value of k for which exactly one pair of integers (a, b) makes the equation true?