Behaghu is 40 years old and her son is twice her daughter’s age. Behaghu will be thrice her son’s age when her daughter is 12 years old. How old will Behaghu be when her 2 children’s combined age equals to her age?

Question

Aurora Arias · Accepted Answer

Behaghu will be 68 years old. See image

I have used a different technique to solve this problem leveraging what is termed "Bar Model" a problem solving technique used in Singapore. It allows to capture the problem statement using a bar a unit bar model. The technique hinges on computing the bar unit that as glue to the algebraic relationships, but no algebra as we know is used (well technically 4u+24=40 is algebra so a small pert of algebra). But note it collapses this relatively cumbersome problem to simple model that pre-algebra student can easily tackle.
It maybe instructive to construct the problem algebraically and verify the answer using algebra.

A couple of things I did like about this technique, I had to use Visio, yuck!

Luna Angel · Answer

undefined Let B represent Behaghu's age, S represent her son's age, and D represent her daughter's age.

Given:
1. B = 40
2. S = 2D
3. B + 3 = 3(S + 12)

From equation 2, we can substitute S = 2D into equation 3:
40 + 3 = 3(2D + 12)

Solve for D:
40 + 3 = 6D + 36
43 = 6D + 36
6D = 43 - 36
6D = 7
D = 7/6

Since D represents the daughter's age, it must be a whole number. Therefore, it implies that D = 1.

From equation 2, S = 2D, we find:
S = 2(1)
S = 2

Thus, the son's age (S) is 2 years.

Now, we find B from equation 1:
B = 40 years.

The combined age of Behaghu's children when it equals her age is:
2 + 1 = 3 years.

So, Behaghu will be 43 years old when her two children's combined age equals her age.