Problem solving

[Guest]

Your father gives one-half of the money in his pocket to your mother, one-fourth of what is left to your brother, and one-third of what is left to your sister. He then splits the remainder with you. If you get $2.00, how much did your father start with?

 

[stapel]

Work backwards. He gave you two dollars. This was half of what he'd had. So how much did he have before giving you the two dollars?

That amount was the two-thirds left over after giving some amount to your sister. So how much did he have before giving her money?

And so forth.

Eliz.

 

[galactus]

This sort of problem makes you scratch your head, doesn't it?.

Let x be the amount your dad starts with. Okey-doke?.

If he gives half away, he has half left. \(\displaystyle x-\frac{x}{2}=\frac{x}{2}\)

Now, he gives one-fourth of this away, \(\displaystyle (x-\frac{x}{2})-(\frac{x}{2}\cdot\frac{1}{4})\)

See?.


\(\displaystyle \frac{x}{2}-\frac{x}{8}=\frac{3x}{8}\)

Now, one-third of that. What is \(\displaystyle \frac{1}{3}\cdot\frac{3x}{8}\)?.

Right. \(\displaystyle \frac{x}{8}\)

Last, since he splits it with you, you have one-half of that amount.

\(\displaystyle \frac{(\frac{x}{2}-\frac{x}{8}-\frac{x}{8})}{2}=\frac{x}{8}\)

So we have:

\(\displaystyle \frac{x}{2}-\frac{x}{8}-\frac{x}{8}-\frac{x}{8}=2\).

\(\displaystyle \frac{x}{2}-\frac{3x}{8}=2\)

\(\displaystyle \frac{x}{8}=2\). Solve for x.

Look what it broke down to!. A simple little equation.

 

[stapel]

See also the replies posted to another thread you started on this exercise.

In the future, please post follow-up questions to the original thread, rather than reposting the exercise. As you'll note upon comparing the two threads, reposting just meant you pretty much got two copies of the same algebra-based solution, rather than the help you'd requested with your fractions. Maintaining one conversational thread can help avoid this sort of mix-up.

Thank you for your consideration.

Eliz.