Question

One positive number is 5 more than twice another. If their product is 1827, find the numbers.

smaller number =
larger number =

Answer 1

9514 1404 393

Answer:

• smaller: 29
• larger: 63

Explanation:

If we let x and y represent "one number" and "another", respectively, then the given relations are ...

x = 5 +2y

xy = 1827

Substituting for x gives a quadratic in y:

(5 +2y)(y) = 1827

2y^2 +5y -1827 = 0 . . . . . written in standard form

We can use the quadratic formula to find the positive value of y that satisfies this:

y = (-5 +√(5² -4(2)(-1827)))/(2(2)) = (-5 +√14641)/4 = 116/4 = 29

x = 5 +2(29) = 63 . . . . using the above expression for x

The smaller number is 29; the larger number is 63.