Question

The sum of the ages of a mother and her
daughter is 50 years. Also 5 years ago, the
mother's age was 7 times the age of the daugh-
ter. The present age of the mother is:​

Answer 1

Step-by-step explanation:

The sum of the ages of a mother and her daughter is 50yrs. Also 5yrs ago, the mother's age was 7 tyms the age of the daughter. What are the present ages of the mother nd daughter?

First, let's break the question down:

The total of the mother's age and the daughter’s age is 50.

5 years ago, the mother was 7 times the age of the daughter.

Therefore,

If the total of their ages is 50 now, then 5 years ago the total of their ages was 40 (50 years minus 5 years off the mother's age and 5 years off the daughter’s age, or 50-(5+5)).

That last point is what will help us solve this problem. Let's state the last point as an equation. For the purposes of crafting some nice tidy equations, I’m going to say that:

M=Mother’s age five years ago

D=Daughter’s age five years ago

The first equation is pretty simple:

M+D=40

We also have to write the part about the mother being 7 times older than the daughter into an equation:

M=7D

Now that we have two equations, we can use them together to solve the question about how old the mother and daughter were 5 years ago. First, we can get rid of M to make the equation easier to solve.

Since M=7D, substitute the M in the first equation with 7D in the second equation:

M+D=40 -> 7D+D=40

Now solve for D.

7D+D=40

8D=40

8D/8=40/8

D=5

So 5 years ago, the daughter was 5 years old. Now extrapolate:

5 years ago the daughter was 5, so now she’s 10.

5 years ago, the mother was 7 times the age of her daughter (7D=M, or 7(5)=M), so 5 years ago the mother was 35, and now she’s 40 (7D+5=Mother’s current age, or 7(5)+5=Mother’s current age)

And if you need more proof,

40+10=50

Answer 2

Question :

The sum of the ages of a mother and her daughter is 50 years. Also, 5 years ago, the mother's age was 7 times the age of the daughter. The present age of the mother is?

$\qquad$_____________

Answer :

The present age of the mother is 40 years.

$\qquad$_____________

Step-by-step explanation:

❍ Let, the daughter's age be z years.

$\:$

It is given that, the sum of their ages is 50 years. So :

➻ Mother's age + Daughter's age = 50

➻ Mother's age + z years = 50

➻ Mother's age = 50 — z years

$\:$

Their ages five years ago will be :

➻ Daughter's age = (z — 5) years

➻ Mother's age = (50 — z — 5) years

$\:$

According to the question, 5 years ago, the mother's age was 7 times the age of daughter.

➻ $~~ \sf{ 7 \: (z-5)= (50- z-5)}$

➻ $~~ \sf{7z-35=50-5-z}$

➻ $~~ \sf{7z + z = 45 + 35}$

➻ $~~ \sf{8z = 80}$

➻ $~~ \sf{z= \cancel \dfrac{80}{8} }$

$\:$

So, substituting z = 10 and finding the mother's age :

➻ Mother's age = (50 — z) years

➻ Mother's age = 50 — 10

➻ Mother's age = 40 years

$~$

$\sf \therefore \: \underline{The \: present~ages \: of \: the \:mother \: and \: the \: daughter \: are \: \pmb{ 40 \: years}\: and \: \pmb{10 \: years} \: respectively. }$