Answer:
The numbers are: 3 and 11
Step-by-step explanation:
Please find the attached.
Answer:
3 and 11
Step-by-step explanation:
Recall what "mean" and "range" are: mean is the average of n numbers, and range is the difference between the greatest value and the least value in a set of n numbers.
They tell us that there are 2 numbers, we can represent them as A and B.
The average is quotient of the sum of n terms and n. In our case, the average is simply,
[tex]\frac{A+B}{2}[/tex] = 7
The range is then,
[tex]A-B=8[/tex]
(since they aren't asking for their individual values we don't need to stress over whether we should do A-B = 8 or B-A = 8)
We can treat both equations as a system of equations!
A + B = 2(7) (multiply both sides by 2)
A + B = 14 (simplify)
We can rearrange the equation in terms of A or B but there's a lazier way we can solve it: elimination! We can subtract A-B = 8 from A + B = 14!
A + B = 14
- (A - B = 8)
2B = 6 -> B = 3
We can plug in the new B value into either equation to find A,
A + 3 = 14 -> A = 11
So our answer is 3 and 11.
Let me know if you have any more questions!
