##### Question

# Your dad is 34 years older than your brother

Your dad is 34 years older than your brother. Five years ago, your dad was three times as old as your brother. How old are they now?

What I know already:

x-y = 34

## Solutions

##### Expert Solution

Let

x=your dad's age (right now)

y=your brother's age (right now)

so this means that

x-5=your dad's age 5 years ago

y-5=your brother's age 5 years ago

Since "Your dad is 34 years older than your brother", this means that {{{x=y+34}}} which can be rewritten as {{{x-y=34}}}. So our first equation is {{{x-y=34}}}

Also, because "Five years ago, your dad was three times as old as your brother", we know that {{{x-5=3(y-5)}}}

{{{x-5=3(y-5)}}} Start with the given equation.

{{{x-5=3y-15}}} Distribute

{{{x=3y-15+5}}} Add 5 to both sides.

{{{x-3y=-15+5}}} Subtract 3y from both sides.

{{{x-3y=-10}}} Combine like terms.

So our second equation is {{{x-3y=-10}}}

So you just need to solve the system

{{{system(x-y=34,x-3y=-10)}}}

to find x and y. I'll let you do that.

If you have any questions, email me at <a href="mailto:</a>.

Check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">website</a> if you are interested in tutoring.

x=your dad's age (right now)

y=your brother's age (right now)

so this means that

x-5=your dad's age 5 years ago

y-5=your brother's age 5 years ago

Since "Your dad is 34 years older than your brother", this means that {{{x=y+34}}} which can be rewritten as {{{x-y=34}}}. So our first equation is {{{x-y=34}}}

Also, because "Five years ago, your dad was three times as old as your brother", we know that {{{x-5=3(y-5)}}}

{{{x-5=3(y-5)}}} Start with the given equation.

{{{x-5=3y-15}}} Distribute

{{{x=3y-15+5}}} Add 5 to both sides.

{{{x-3y=-15+5}}} Subtract 3y from both sides.

{{{x-3y=-10}}} Combine like terms.

So our second equation is {{{x-3y=-10}}}

So you just need to solve the system

{{{system(x-y=34,x-3y=-10)}}}

to find x and y. I'll let you do that.

If you have any questions, email me at <a href="mailto:</a>.

Check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">website</a> if you are interested in tutoring.

answered by: dinesh