Five years ago, Matt is twice as old as his brother. How old are they now if the product of their ages is 375?

[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} [/tex]

SOLUTION:

Let x be the age of Matt's brother five years ago.

AGES 5 YEARS AGO

Matt's brother - x
Matt - 2x

AGES AT PRESENT

Matt's brother - x + 5
Matt - 2x + 5

If the product of their ages at present time is 375, then we'll have an equation of: [tex]\rm( 2x + 5)(x + 5) = 375 [/tex].

[tex]\rm( 2x + 5)(x + 5) = 375 [/tex]

[tex]\rm2x {}^{2} + 10x + 5x + 25= 375 [/tex]

[tex]\rm2x {}^{2} + 15x+ 25= 375 [/tex]

[tex]\rm2x {}^{2} + 15x= 375 - 25 [/tex]

[tex]\rm2x {}^{2} + 15x= 350[/tex]

[tex]\rm2x {}^{2} + 15x - 350 = 0[/tex]

[tex]\rm2x {}^{2} + 35x - 20x- 350 = 0[/tex]

[tex]\rm x(2x + 35)- 10(2x + 35)= 0[/tex]

[tex]\rm (2x + 35)(x- 10)= 0[/tex]

[tex] \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \rm 2x + 35= 0[/tex]

[tex]\boxed{\rm x = - \frac{35}{2}} [/tex]

[tex] \overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \rm x - 10 = 0[/tex]

[tex]\boxed{\rm x = 10}[/tex]

• Since we're talking about ages, we'll focus only on 10 being the value of x.

[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} [/tex]

ANSWER:

AGES 5 YEARS AGO

Matt's brother - x = 10
Matt - 2x = 20

AGES AT PRESENT

Matt's brother - x + 5 = 15
Matt - 2x + 5 = 25

> Therefore, at present time, Matt is 25 years old while his brother is 15 years old.

[tex] \blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} [/tex]