Question

The sum of Amber's and henry's ages is 17 four times henry's age is nine less than the square of Amber's age. what are their ages? full solution AND THE MATHEMATICAL STATEMENT TY​

Answer 1

Answer:

The age of Amber is 7 years and the age of Henry is 10 years

Step-by-step explanation:

Given :

• The sum of Amber's and Henry's ages is 17
• Four times Henry's age is nine less than the square of Amber's age.

To find :

their ages

Solution :

Let the age of Amber be x years and the age of Henry be y years.

⮞ The sum of Amber's and Henry's ages is 17

  x + y = 17

  y = 17 - x ➙ [1]

⮞ Four times Henry's age is nine less than the square of Amber's age.

  4 × y = x² - 9

  4y = x² - 9

  x² - 4y - 9 = 0 ➙ [2]

Put y = (17 - x) in equation [2]

 x² - 4(17 - x) - 9 = 0

 x² - 68 + 4x - 9 = 0

 x² + 4x - 77 = 0

 x² + 11x - 7x - 77 = 0

 x(x + 11) - 7(x + 11) = 0

(x + 11) (x - 7) = 0

⇒ x + 11 = 0 ; x = -11

⇒ x - 7 = 0 ; x = 7

Age can not be negative. Hence, x ≠ -11

∴ x = 7

Value of y :

x + y = 17

7 + y = 17

y = 17 - 7

y = 10

Therefore, the age of Amber is 7 years and the age of Henry is 10 years

Answer 2

Step-by-step explanation:

$\huge\sf\underline\blue{answer}$

$\huge\bf\underline\green{given}$

1) sum of Amber's and henry's ages is 17

2) four times henry's age is nine less than the square of Amber's age.

$\huge\fcolorbox{black}{pink}{solution}$

let,

the age of

amber be : x

Henry be : y

according to question,

x+y = 17

.: y = 17-x

[let it be equation 1]

.: 4y = x²-9

.: substituting value of y :

4(17-x) = x²-9

68-4x = x²-9

x²-9-68+4x = 0

x²+4x-77 = 0

x²+11x-7x-77 = 0

x(x+11)-7(x+11) = 0

(x+11) (x-7) = 0

.: x+11 = 0 (or) x-7 = 0

x = -11 (or) x = 7

.: age can't be negative so, x = 7

.: age of amber'x' = 7

age of henry 'y' = 17-7 = 10

.: age of amber = 7years

age of henry = 10years