The sum of two numbers is 30 and their difference is 12.what are the 2 numbers?

1 Answer
Apr 10, 2018

The two numbers are 21 and 9

Explanation:

Let the two numbers be a and b

The sum of these numbers is 30
a + b = 30

The difference between these numbers is 12
a - b = 12

color(white)(mmmmmmmm)―――――――――

I.  You can solve this by logic.

If the two numbers were exactly equal, then they would both be 15.
15 + 15 = 30

But the difference would be 0, not 12

So if you lowered b by one point, and added that to a, then the two numbers would be 16 and 14, and the difference would be 2.

So you can see that for every point you subtract from b to add to a, you increase the distance between them by 2

So, by logic, you need to subtract 6 points from b and add them to a to create a difference of 12

(15 + 6) minus (15 - 6) gives a difference of 12
color(white)(.m)21 color(white)(.....) - color(white)(mmnn)9        =   12

Answer:
The two numbers are 21 and 9

color(white)(mmmmmmmm)―――――――――

II.  You can solve this by math

These are simultaneous equations, so you can solve them by math.

color(white)(.)a + b = 30
color(white)(.)a - b = 12
color(white)()――――――
2acolor(lightgray)( + 0)=42
color(white)(.)a          = 21 larr same answer