Alright, let's solve this problem step by step.
Let [tex]\( p \)[/tex] be the cost of one plate and [tex]\( b \)[/tex] be the cost of one bowl.
First, we are given that the cost of 10 plates is the same as the cost of 4 bowls. We can set this up as an equation:
[tex]\[ 10p = 4b \][/tex]
Next, we need to determine how many bowls would cost the same as 9 plates. Let's call this number [tex]\( k \)[/tex]. Thus:
[tex]\[ 9p = kb \][/tex]
We will use the first equation to express [tex]\( p \)[/tex] in terms of [tex]\( b \)[/tex]. From the equation:
[tex]\[ 10p = 4b \][/tex]
Dividing both sides by 10, we get:
[tex]\[ p = \frac{4b}{10} = \frac{2b}{5} \][/tex]
Now, we substitute this value of [tex]\( p \)[/tex] into the second equation:
[tex]\[ 9p = kb \][/tex]
[tex]\[ 9 \left(\frac{2b}{5}\right) = kb \][/tex]
Simplify this equation:
[tex]\[ \frac{18b}{5} = kb \][/tex]
To isolate [tex]\( k \)[/tex], we divide both sides by [tex]\( b \)[/tex]:
[tex]\[ \frac{18}{5} = k \][/tex]
[tex]\[ k = \frac{18}{5} \][/tex]
[tex]\[ k = 3.6 \][/tex]
Since [tex]\( k \)[/tex] represents the number of bowls, and this is a practical scenario dealing with whole items, we round [tex]\( k \)[/tex] to the nearest whole number.
Thus, the number of bowls that would cost the same as 9 plates is [tex]\( 4 \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
