Question

9) The ages of three sisters in a family can be expressed as consecutive integers. The product of twice the age of the youngest sister and the age of the middle sister is four more than 8 times the age of the oldest sister. Find the ages of the three sisters.​

Answer 1

Answer

let's say S is the age of the youngest sister. Then the age of the middle sister is S + 1, and the age of the oldest sister compared to the youngest is S + 2

we have

54 = S + (S+1) + (S+2)

which is the same as

54 = 3S + 3

divide both sides by 3

54 / 3 = S + 1

18 = S + 1

subtract one from both sides

17 = S

check

54 = 17 + 18 + 19

Answer 2

Step-by-step explanation:

Given :-

The ages of three sisters in a family can be expressed as consecutive integers. The product of twice the age of the youngest sister and the age of the middle sister is four more than 8 times the age of the oldest sister.

To find :-

Find the ages of the three sisters?

Solution :-

Given that :

The ages of three sisters in a family can be expressed as consecutive integers

Let they be X ,X+1 and X+2

Let the age of Younger sister be X years

Let the age of Middle sister be (X+1) years

Let the age of Oldest sister be (X+2) years

Given that

The product of twice the age of the youngest sister and the age of the middle sister is four more than 8 times the age of the oldest sister.

=> 2×Younger sister's age × Middle sister's age =

8×Oldest sister's age + 4

=>( 2×X) × (X+1) = 8×(X+2)+4

=>2X(X+1) = 8(X+2)+4

=> 2X²+2X = 8X+16+4

=> 2X²+2X = 8X+20

=> 2X²+2X-8X-20 = 0

=> 2X²-6X-20 = 0

=> 2(X²-3X-10) = 0

=> X²-3X-10 = 0/2

=>X²-3X-10 = 0

=> X²+2X-5X-10 = 0

=> X(X+2)-5(X+2) = 0

=> (X+2)(X-5) = 0

=> X+2 = 0 or X-5 = 0

=> X = -2 or X = 5

X can not be negative

=> X = 5 years

=> X+1 = 5+1 = 6 years

=> X+2 = 5+2 = 7 years

Therefore, their ages 5 years , 6 years , 7 years

Answer:-

The age of Younger sister = 5 years

The age of Middle sister = 6 years

The age of Oldest sister = 7 years

Check :-

5,6,7 are the Consecutive numbers

2×Younger sister's age × Middle sister's age

= 2×5×6

= 10×6

= 60 years

and

8×Oldest sister's age + 4

= 8×7+4

= 56+4

= 60 years

So ,

The product of twice the age of the youngest sister and the age of the middle sister is four more than 8 times the age of the oldest sister.

Verified the given relations in the given problem.