# Ratio help

• April 29th 2009, 07:44 AM
pri
Ratio help
1/5 of chicken John had is equal to 3/4 of Mark.
John sold 150 chickens while Mark bought 160.
The remider is in a ratio of 5:3, for John & Mark respectively.
What was the total number of chickens both had at first.
• April 29th 2009, 08:00 AM
Unenlightened
Quote:

Originally Posted by pri
1/5 of chicken John had is equal to 3/4 of Mark.
John sold 150 chickens while Mark bought 160.
The remider is in a ratio of 5:3, for John & Mark respectively.
What was the total number of chickens both had at first.

Let J be the amount John had at the start, and let M be the amount Mark had at the start.
So J/5 = 3M/4

Then if J' is the amount that John had after the buying and selling, and M' is the amount Mark had after buying and selling, then the 5:3 ratio tells us that
3J'/8 = 5M'/8

We also know that J' = J - 150
and M' = M + 160.

So if we replace J' and M' with those
we get:
$\frac{3(J - 150)}{8} = \frac{5(M + 160)}{8}$

So we have two simultaneous equations with two unknowns:
$\frac{3(J - 150)}{8} = \frac{5(M + 160)}{8}$
$\frac{J}{5} = \frac{3M}{4}$

And solve...
• April 29th 2009, 08:04 AM
Twig
hi
hi!

Let $C_{j} \mbox{ and } C_{m}$ be notations for chickens for John and for Mark.

We have that:

$\frac{1}{5}C_{j}=\frac{3}{4}C_{m} \Rightarrow 4C_{j}-15C_{m}=0$

We have also:

$\frac{C_{j}-150}{C_{m}+160}=\frac{5}{3} \Rightarrow 3C_{j}-5C_{m}=1250$

So, you have two equations and two unknowns. Can you proceed from here?