Question

Please use a system of equations to solve this problem. I already know how to solve this, but I want to know how to solve it using a system of equations!!! A writing workshop enrolls novelists and poets in a ratio of 5:3. There are 24 people at the workshop. How many novelists are there and how many poets are there?

Answer 1

`\boxed{\sf \ \ \ 15 \ \ novelists \ \ and \ \ 9 \ \ poets \ \ \ }`

Explanation:

hello,

let's note a the number of novelists and

b the number of poets.

we know that a = 5/3 b as "enrolls novelits and poets in a ratio of 5:3"

it comes 3a=5b which is the first equation

and we know that a + b = 24 "there are 24 people"

we we have two equations

(1) 3a - 5b = 0

(2) a + b = 24

let's multiply (2) by 3 it comes 3a + 3b = 24*3 = 72

let's do 3*(2) - (1) it comes

3a + 3b -3a + 5b = 72 - 0 = 72

so 8b = 72

so b = 9

and then we replace b in (2) it comes

a = 24-9 = 15

hope this helps