Name: marcee
Who is asking: Other
Level of the question: All

Question: Hello!

I hope you can help me.

If you take $20 from the first and put it into the second of three purses, the second would then contain 4 times as much as remains in the first. If $60 of what is now in the second is put into the third, the third will contain twice what is in the first and second together. Now, if $40 be removed from the third and put into the first, there will be half as much as in the third. What did each purse originally hold?

I know the answer but cannot work it out.

Thanks
marcee

 

Hi Marcee,

I let f be the amount of money in the first purse, s the amount of money in the second purse and t the amount of money in the third purse. I am going to keep track of the three steps in this procedure using a table

  Purse one Purse two Purse three
Start $f $s $t
Step 1 $f - $20 $s + $20 $t
Step 2 $f - $20 $s + $20 - $60 $t + $60
Step 3 $f - $20 + $40 $s + $20 - $60 $t + $60 - $40

The instructions say that after the first step "the second would then contain 4 times as much as remains in the first". Thus

$s + $20 = 4 ($f - $20)

After the second step "the third will contain twice what is in the first and second together". Thus

$t + $60 = 2( $f - $20 + $s + $20 - $60)

After the third step "there will be half as much (in the first purse) as in the third".

Write the equation fir this step and then solve the three equations for $f, $s and $t

Penny