# Thread: worded problems

1. ## 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!

2. For the first one let Phil's money be $\displaystyle P$ and Jill's money be $\displaystyle J$

The two equations you get from this information are:

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

and

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

Solve these equations simultaneously to get the solutions.

3. Hi,

Thanks for the reply. I got up to that stage. I guess my problem is solving the equation.

4. Oh,

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

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

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

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

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

$\displaystyle 5P=1800$

$\displaystyle P=360$

Now if you plug this value of $\displaystyle P$ into one of the first two equations you'll also get the solution for $\displaystyle J$

5. 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?

6. 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.

7. 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

8. Your method is correct, except for the last step.

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

$\displaystyle \therefore 5P=1800$

$\displaystyle \therefore P=360$

9. Damn, so simple.

cheers for the help.