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:
$\displaystyle \frac{3(J - 150)}{8} = \frac{5(M + 160)}{8}$
So we have two simultaneous equations with two unknowns:
$\displaystyle \frac{3(J - 150)}{8} = \frac{5(M + 160)}{8}$
$\displaystyle \frac{J}{5} = \frac{3M}{4}$
And solve...
hi!
Let $\displaystyle C_{j} \mbox{ and } C_{m} $ be notations for chickens for John and for Mark.
We have that:
$\displaystyle \frac{1}{5}C_{j}=\frac{3}{4}C_{m} \Rightarrow 4C_{j}-15C_{m}=0 $
We have also:
$\displaystyle \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?