Question

Marco is 8 years younger than his brother Paolo. If their product of their ages is 105, how old is Marco? plz help

Answer 1

Marco's age is 7 years old

Explanation:

Let

x ----> Marco's age

y ----> Paolo's age

we know that

`x=y-8` ---->
`y=x+8` ----> equation A

`xy=105` ----> equation B

substitute equation A in equation B

`x(x+8)=105`

`x^2+8x-105=0`

Solve the quadratic equation

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

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

in this problem we have

`x^2+8x-105=0`

so

`a=1\\b=8\\c=-105`

substitute in the formula

`x=\frac{-8(+/-)\sqrt{8^(2)-4(1)(-105)}} {2(1)}`

`x=\frac{-8(+/-)√(484)} {2}`

`x=\frac{-8(+/-)22} {2}`

`x=\frac{-8(+)22} {2}=7`

`x=\frac{-8(-)22} {2}=-15`

Remember that the solution cannot be a negative number

so

The solution is x=7

therefore

Marco's age is 7 years old