The sum of two positive integers is 42. When the smaller integer is subtracted from twice the larger the result is 24. Find the two integers

Question

The sum of two positive integers is 42. When the smaller integer is subtracted from twice the larger the result is 24. Find the two integers

Answer 1

x represents the larger number

42 - x represents the smaller number

2x - (42 - x) = 24

Can you solve for x and answer?

Answer 2

Alternatively:

x + y = 42

2x - y = 24

If I add y to both sides of this equation, I get:

2x = 24 + y

and then further simplify by dividing both sides by 2 to get:

x = (24 + y)/2

If I substitute the right hand side of this equation for 'x' in the first equation, I get:

(24+y)/2 + y = 42

From here, I can multiply both sides of the equation by 2 to get rid of the denominator:

24 + y + 2y = 84

and combine like terms to get:

24 + 3y = 84

If I take 24 from both sides, I get:

3y = 60

and then solving for y is quite simple :)

Once you have a value for 'y', you can substitute that value into the first equation and solve for 'x' in a single step.

Best of luck!