Answer:
The two numbers are 10 and 7.
Step-by-step explanation:
Given:
The two numbers whose difference is three, when the larger number is decreased by three times the smaller number the result is -11.
Now, find the two numbers.
Let the larger number be [tex]x[/tex].
Let the smaller number be [tex]y[/tex].
As given, the two numbers whose difference is three:
[tex]x-y=3[/tex]
[tex]x=3+y[/tex]
So, the value of [tex]x=3+y[/tex].
According to question:
[tex]x-3y=-11[/tex]
Putting the value of [tex]x[/tex] we get:
[tex]3+y-3y=-11[/tex]
[tex]3-2y=-11[/tex]
Moving variables on one side and the number on the other we get:
[tex]3+11=2y[/tex]
[tex]14=2y[/tex]
Dividing both sides by 2 we get:
[tex]7=y[/tex]
The smaller number = 7.
Now, putting the value of [tex]y[/tex] in the equation [tex]x-y=3[/tex]:
[tex]x-y=3[/tex]
[tex]x-7=3[/tex]
Adding both sides by 7 we get:
[tex]x=10.[/tex]
The larger number = 10.
Therefore, the two numbers are 10 and 7.
