the sum of the ages of rex, ben and alfred is 36 years, two years ago, ben was 3 times as old as rex was then, 8 years from now, alfred will be twice as old as ben will be then. find their present age.

Question

the sum of the ages of rex, ben and alfred is 36 years, two years ago, ben was 3 times as old as rex was then, 8 years from now, alfred will be twice as old as ben will be then. find their present age.

Answer 1

let's see what they told you:

r+b+a = 36
b-2 = 3(r-2)
a+8 = 2(b+8)

Now just solve for the ages.

Answer 2

Let's solve the problem step-by-step:

Step 1: Assign variables
Let's assume Rex's present age is R years, Ben's present age is B years, and Alfred's present age is A years.

Step 2: Translate the given information into equations
From the given information, we have two equations:

Equation 1: The sum of their ages is 36
R + B + A = 36

Equation 2: Two years ago, Ben was 3 times as old as Rex was then
B - 2 = 3(R - 2)

Step 3: Simplify equation 2
B - 2 = 3R - 6
B = 3R - 4

Step 4: Substitute equation 2 into equation 1
R + (3R - 4) + A = 36
4R - 4 + A = 36
4R + A = 40

Step 5: Solve equations 3
R + (3R - 4) + A = 36
4R + A = 40

To solve this system of equations, we can either use substitution or elimination method. Let's use substitution method:

Substitute A in equation 4 with (40 - 4R):

4R + (40 - 4R) = 40
40 = 40

The equation becomes redundant and does not provide any information about the ages. This means that there are infinite solutions to this problem.

Therefore, we cannot determine their present ages with the given information.

Answer 3

To solve this problem, we can set up a system of equations.

Let's say that Rex's age is R, Ben's age is B, and Alfred's age is A.

We're given two pieces of information:
(1) The sum of their ages is 36 years: R + B + A = 36
(2) Two years ago, Ben was three times as old as Rex was then: B - 2 = 3(R - 2)

To solve this system of equations, we need to find the values of R, B, and A that satisfy both equations.

Let's solve equation (2) for B in terms of R:
B = 3(R - 2) + 2
B = 3R - 6 + 2
B = 3R - 4

Now substitute this value into equation (1):
R + (3R - 4) + A = 36
4R + A = 40
A = 40 - 4R

Substituting A = 40 - 4R into equation (1):
R + (3R - 4) + (40 - 4R) = 36
8R + 36 = 36
8R = 0
R = 0

If R = 0, then from equation (2):
B = 3(0 - 2) + 2
B = -4

And from equation (1):
0 + (-4) + A = 36
A = 36 + 4
A = 40

However, since we cannot have negative ages, it means there is no solution to this problem.