Question

one third the difference of two number is 12. if the larger number is 9, what is the sum of the two numbers

Answer 1

x=smaller number

y=larger number

x+y=12

y=3x-6

Let's begin with the first equation...

x+y=12

Let's substitute...

x+(3x-6)=12

4x-6=12

Let's add 6 to both sides as we proceed to isolate x...

6+4x-6=12+6

4x=18

Let's divide both sides by 4...

(4x)/4=18/4

x=9/2=4.5---smaller number

12-4.5=7.5s larger number

Answer 2

The sum of the two numbers is -18.

Explanation:

You can work your way through the problem starting with ...

1/3 the difference of two numbers is 12

Since 3 times 12 is 36, the difference of the two numbers is 36.

Then you are told ...

the larger number is 9

so the smaller number will be 9 less the difference, or ...

smaller number = 9 - 36 = -27.

Now, you know both numbers, so you know there sum is ..

9 + (-27) = -18 . . . . . sum of the two numbers

_____

You can work it also using L for the larger number, D for the difference. Then the smaller number is (L-D) and the sum is ...

sum = L + (L -D) = 2L - D

Filling in the values given for the larger number and the difference, you have ...

sum = 2·9 - 3·12 = 18 -36 = -18 . . . . . as before