MHB How old until mother is 4 times older

[Johnx1]

Junhao's sister is 5 years old. She is 36 years younger than their mother. In how many years' time will their mother's age be 4 times her age?

My answer: I'm not sure how to create an algebraic expression for this.

 

[HOI]

Let "S" be Junhao's sister's age. Let "M" be their mother's age.

"She is 36 years younger than their mother." So S= M- 36.

"In how many years' time will their mother's age be 4 times her age?"

In "t" years, the sister's age will be S+t and the mother's age will be M+ t. Their mother's age will be 4 times her age when M+ t= 4(S+ t).

Those are the equations representing this situation. You can reduce this to a single equation by replacing S in the second equation with M- 36, from the first equation:
M+ t= 4(M- 36+ t)= 4M- 144+ 4t which can be written as 3M+ 3t= 144 or, dividing by 3, M+ t= 48.

That is a single equation in the two unknowns, M and t, so it is not possible to solve for specifiic values of M and t. There are many different values of M, S, and t that satisfy these conditions but we can say that, however many years that will be in the future, the mother will be 48 and the sister 12. Of course, at any age the sister will be 36 years younger than the mother- that doesn't change.

 

[Wilmer]

Junhao's sister is 5 years old.
She is 36 years younger than their mother.
In how many years' time will their mother's age be 4 times her age?

S=sister's age, M=mother's age, Y = years

Given:
S = 5, M = 5+36 = 41

4(S + Y) = M + Y
4(5 + Y) = 41 + Y
20 +4Y = 41 + Y
3Y = 21
Y = 7

5+7=12; 12*4 = 48
41+7 = 48

 

[Johnx1]

S = sister
M = mother

so,

s = M - 36
m = 4s

s = 4s -36
s = 12

m = 4(12)

so the mother has to be 48.Thank you.