# worded problems

• Nov 27th 2009, 07:15 PM
aquajam
worded problems
Can someone help me put this into equations and solve them:

1. Phil has $150 and three-quarters of what Jill has, and Jill has$100 and half of what Phil has, so how much have each?

2. If a teacher can place her students four to a table, there will be three students on the final table. But, if five children are placed on each table, there will be four students on the the last table.

What is the smallest number of children the class could have?

Thanks!
• Nov 27th 2009, 07:41 PM
Stroodle
For the first one let Phil's money be $P$ and Jill's money be $J$

The two equations you get from this information are:

$P=150+\frac{3}{4}J$

and

$J=100+\frac{1}{2}P$

Solve these equations simultaneously to get the solutions.
• Nov 27th 2009, 07:44 PM
aquajam
Hi,

Thanks for the reply. I got up to that stage. I guess my problem is solving the equation.
• Nov 27th 2009, 07:54 PM
Stroodle
Oh,

If you plug the second equation into the first one you get:

$P=150+\frac{3}{4}\left (100+\frac{1}{2}P\right )$

$4P=600+3\left (100+\frac{1}{2}P\right )$ (multiplied everything by 4)

$4P=600+300+\frac{3}{2}P$

$8P=1200+600+3P$ (multiplied everything by 2)

$5P=1800$

$P=360$

Now if you plug this value of $P$ into one of the first two equations you'll also get the solution for $J$
• Nov 27th 2009, 08:01 PM
aquajam
Ah, thanks.

How do you determine to multiply by 8 and 4? To bring the fractions to integers?

I was trying with substitution, but when multiplying out the first line (before multiply x 8) I would get the wrong answer. As a side question, why doesn't that work?
• Nov 27th 2009, 08:07 PM
Stroodle
To clear the fractions you just multiply the equation by the denominator of the fraction in question.
As far as I'm aware the method I used is called substitution, but if you post your working here we can try to see where you went wrong.
• Nov 27th 2009, 08:15 PM
aquajam
I was attempting to do it this way:

(sorry couldn't get the math code to work)

p = 150 + 3/4 (100 + 1/2p )

p = 150 + 75 + 3/8P

P = 225 + 3/8p

225 = 5/8p

p = 309.37
• Nov 27th 2009, 08:26 PM
Stroodle
Your method is correct, except for the last step.

$\frac{5P}{8}=225$

$\therefore 5P=1800$

$\therefore P=360$
• Nov 27th 2009, 08:44 PM
aquajam
Damn, so simple.

cheers for the help.