Question

question 10 of 10 step 1 of 1 00:42:41 the product of two positive integers is 44, and their sum is 15. what are the integers? answerhow to enter your answer (opens in new window) 2 points keypad keyboard shortcuts

Explanation:

Step1: Define variables for integers

Let the two positive integers be $x$ and $y$.

Step2: Set up system of equations

We know:
$x + y = 15$ and $xy = 44$
Rearrange $x + y = 15$ to $y = 15 - x$.

Step3: Substitute into product equation

Substitute $y = 15 - x$ into $xy = 44$:
$x(15 - x) = 44$
Expand: $15x - x^2 = 44$
Rewrite as quadratic: $x^2 - 15x + 44 = 0$

Step4: Factor quadratic equation

Factor: $(x - 4)(x - 11) = 0$
Solve for $x$: $x = 4$ or $x = 11$

Step5: Find corresponding y values

If $x=4$, $y=15-4=11$; if $x=11$, $y=15-11=4$.

Answer:

4 and 11