Age problem

Question

Anna's mother is seven less than thrice of Ana's age. Five years ago, Ana's age is five more than one-fifth of her mother's age. Find Ana's and her mother's age.

Answer 1

Let m= mother's age

Let a = Ana's age

 

m = 3a-7   Ana's mother is 7 less than thrice Ana's age

a-5  = (m-5)/5 + 5  Ana is 5 more than 1/5 her mother's age

                              5 years ago

 

We have each variable in terms f the other.

Substitute 3a-7 in place of m in 2nd equation.

 

a -5 = (3a-7-5)/5 + 5 subtract 5 from both sides

a-10 = (3a-12)/5      multiply both sides by 5

5(a-10) = 3a-12       distribute the 5 through 

5a-50 = 3a-12.         subtract 3a from both sides

2a-50 = -12.            add 50 to both sides

2a = 38.                  divide both sides by 2

a= 19

 

Ana is 19 years old

 

m = 3a-7

m = 3(19)-7

m = 57-7

m = 50

 

Ana's mother is 50 years old.

 

 

Answer 2

Hi Krista,

 

M = Anna's mother's age

A = Anna's age

M-5 = Anna's mother's age 5 years ago

A-5 = Anna's age 5 years ago

 

The first sentence tells us

M = 3A-7

 

From the 2nd sentence we have

A-5 = (M-5)/5 + 5

 

Substitute M = 3A-7 in the 2nd equation.

 

A-5 - (3A-7-5)/5+5

 

Then solve for A

A-5 = (3A-12)+5

A-10 = (3A-12)/5

5(A-10) = 3A-12

5A-50 = 3A-12

2A = 38

A  = 19

 

And since M = 3A-7

M = 3(19) = 7

M = 57-7=50

 

Anna is 19 and her mother is 50.