Question

1. the sum of two integers is 36, where the larger integer is 6 less than two times the smaller integer. what is the larger integer?

Explanation:

Step1: Define variables for integers

Let the smaller integer be $x$, the larger integer be $y$.

Step2: Set up system of equations

From the problem:

1. Sum of integers: $x + y = 36$
2. Larger integer relation: $y = 2x - 6$

Step3: Substitute $y$ into first equation

$x + (2x - 6) = 36$

Step4: Simplify and solve for $x$

$3x - 6 = 36$
$3x = 36 + 6 = 42$
$x = \frac{42}{3} = 14$

Step5: Calculate larger integer $y$

$y = 2(14) - 6 = 28 - 6 = 22$

Answer:

22