Simplify this answer?

Question

[5(b-n)]+[a-n]=64
=5b-5n+a-n=64
=5b+a-5n-n=64
5b+a-6n=64
Find a,b,n

Answer 1

You aren't approaching the problem correctly.

The statement is, "A is 5 times as old as B was, when A was as old a B is now. Current ages sum to 64. Find their current ages."

Let n be the number of years that have passed.
Let A be age of A now.
Let B be age of B now.

'n' years ago, A's age was B's age then.
A - n = B

Current ages sum to 64.
A + B = 64

A is 5 times as old B was 'n' years ago.
A = 5(B - n)

Three equations, three unknowns...
To solve start by solving for one of the variables in terms of the others:
n = A - B

Now substitute n into the last equation:
A = 5(B - (A-B))
A = 5(B - A + B)
A = 5(2B - A)
A = 10B - 5A
6A = 10B
3A = 5B

Now solve for one of the variables (e.g. B)
B = (3/5)A

And substitute into the second equation:
A + (3/5)A = 64
(5/5)A + (3/5)A = 64
(8/5)A = 64

Now multiply both sides by 5/8:
A = 64(5/8)
A = 40

And solve for B:
40 + B = 64
B = 64 - 40
B = 24

Note: Sixteen years ago, A was 24 (same as B now) and B was 8. That makes A five times as old as B was then.

So A is 40 years old and B is 24 years old.

Answer 2

Well, you should know 1 most important. Number of equations should always be more than the umber of unknowns.

But you have given 1 equation with 3 unknowns. All you can get is a, b & n in terms of the rest.

a = 64 + 6n - 5b
b = (64 + 6n - a)/5
n = (5b + a - 64)6