The difference between two numbers is 12. The larger number is 6 less than three times the smaller number. Find both numbers

Question

I'm seriously confused and I need help on setting this up.

How do you solve it and please explain the steps. 

Answer 1

Hi Salma;

I love these questions!  Thank you!

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=7.5---larger number

 

Let's check our work.

3x-6=y

3(4.5)-6=7.5

13.5-6=7.5

7.5=7.5