If we divide the number of novelists by the number of poets, the quotient is always equal to 53.
Novelists: 15 Poets: 9
Practice makes perfect
Let n and p be the number of novelists and poets enrolled, respectively. Since they are in a ratio of 5: 3, then n divided by p is always equal to 5 3.
n/p = 5/3
Before finding our second equation, let's rewrite the equation above so that we do not have to deal with fractions.
On the other hand, we are told that there are 24 people at the workshop. This implies that the sum of the number of novelists and the number of poets equals 24.
n+p=24
The two equations written above form a system of equations that models the described situation.
3n-5p=0 & (I) n+p=24 & (II)
We can solve this system using the Elimination Method. To do that, first we need to multiply Equation (II) by 5. That way, when we add the equations, the p-terms will cancel each other out.
3n-5p=0 5(n+p)=5(24) ⇒ 3n-5p=0 5n+5p=120
With this, we can see that the p-terms will eliminate each other if we add Equation (I) to Equation (II).
