Find two integers whose product is 405 such that one of the integers is three less than twice the other integer.
A)16, 26
B)14, 26
C)15, 27
D)16, 28
E)14, 28

Question

Quizplus · Accepted Answer

Let's call the two integers x and y. We know that xy = 405. We are also told that one of the integers (let's say x) is three less than twice the other integer (y). So we can write an equation: x = 2y - 3. Now we can substitute this expression for x into the first equation:

(2y - 3)y = 405

Expanding and simplifying:

2y^2 - 3y - 405 = 0

Factoring:

(2y + 27)(y - 15) = 0

So y = 15, which means x = 2(15) - 3 = 27. Therefore, the two integers are 15 and 27, which is choice C.

Find Two Integers Whose Product Is 405 Such That One