Draw the number line model and find the quotient
[tex]$5 \div \frac{2}{3}$[/tex]
Answer (3)
In a writing workshop with a ratio of 5:3 novelists to poets and a total of 24 people, there are 15 novelists and 9 poets. ;
Given the ratio of novelists to poets in a writing workshop is 5:3, we can set up a system of equations to determine how many novelists and poets are attending. If n represents the number of novelists and p represents the number of poets, we can derive the following equations from the ratio and total participants:
5_n_ = 3_p_ (ratio of novelists to poets)
n + p = 24 (total number of participants)
To solve this system of equations, we can use the substitution method. First, solve the second equation for n :
n = 24 - p
Now, substitute this expression for n into the first equation:
5(24 - p ) = 3_p_
120 - 5_p_ = 3_p_
Adding 5_p_ to both sides gives us:
120 = 8_p_
Dividing both sides by 8 yields:
p = 15
Therefore, there are 15 novelists in the workshop. Substitute this back into the equation for n :
n = 24 - 15 = 9
So there are 9 poets in the workshop. The system is now solved, showing there are 15 novelists and 9 poets.
In the writing workshop, there are 15 novelists and 9 poets. This is found by setting up a system of equations based on the given ratio of 5:3 and the total number of participants, which is 24. Solving the equations, we determine both counts accurately.
;
