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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?

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Answer:

There are 15 novelists and 9 poets

Step-by-step explanation:

x= novelists and y= poets

x+y = 24

There are 5 novelists for every 3 poets, to balance we multiply by the opposite to make them equal

3x = 5y

Solve for x

x = 5/3 y

Substitute into the first equation

5/3 y +y = 24

5/3y + 3/3y =24

8/3y = 24

Multiply by 3/8

3/8 *8/3 y = 24 * 3/8

y = 9

x+y = 24

x+9=24

x = 15

There are 15 novelists and 9 poets

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