Question

Jos is 33 younger than his father. The product if their ages is 658. How old is Jos?

Answer 1

Answer: Jos is 14 years old

Explanation:

Let Jos is x years old

Hence, father is (x+33) years old

`x(x+33)=658\\\\x^2+33x=658\\\\x^2+33x-658=658-658\\\\x^2+33x-658=0\\\\a=1 \ \ \ \ \ b=33\ \ \ \ \ c=-658`

`\displaystyle\\x=(-bб√(D^) )/(2a) \\\\D=b^2-4ac\\\\D=33^2-4(1)(-658)\\\\D=1089+2632\\\\D=3721\\\\√(D)=\\\\ √(3721)=\\\\61\\\\ x=(-33б61)/(2(1))\\\\ x=(-33-61)/(2)\\\\x=-47\\otin\\\\x=(-33+61)/(2) \\x=(28)/(2) \\\\x=14`

Answer 2

Jos is 14 years

Explanation:

Let Father's age be x

`{ \tt{father = x}} \\ { \tt{jos = x - 33}}`

- The question says, product of their ages is 658

`{ \tt{x(x - 33) = 658}}`

- Open the brackets following distributive property;

-

`{ \tt{ {x}^(2) - 33x = 658 }} \\ { \tt{ {x}^(2) - 33x - 658 = 0 }}`

- Using bulldozer method;

`{ \tt{x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac } }{2a} }} \\`

- A general quadratic equation has a format ax² + bx + c = 0

• b is -33
• a is 1
• c is -658

`{ \tt{x = \frac{ - ( - 33) \pm \sqrt{ {( - 33)}^(2) - (4 * 1 * - 658)} }{2 * 1} }} \\ \\ { \tt{x = (33 \pm √(3721) )/(2) }} \\ \\ { \tt{x = (33 \pm61)/(2) }} \\ \\ { \tt{x = (33 + 61)/(2) \: \: or \: \: (33 - 61)/(2) }} \\ \\ { \tt{x = 47 \: \: \: or \: \: \: - 14}}`

- Father's age = 47 years

- Jos's age = (47 - 33) = 14 years