First, we need to understand the proportional relationship between white flowers and pink flowers in Molly's garden. From the table, we can observe that the relationship between white flowers (x) and pink flowers (y) can be defined as [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
Let's calculate the constant of proportionality (k) using the given table data. We have four pairs of values:
- For the pair (12, 18):
[tex]\[
k = \frac{y}{x} = \frac{18}{12} = 1.5
\][/tex]
- For the pair (24, 36):
[tex]\[
k = \frac{y}{x} = \frac{36}{24} = 1.5
\][/tex]
- For the pair (36, 54):
[tex]\[
k = \frac{y}{x} = \frac{54}{36} = 1.5
\][/tex]
- For the pair (48, 72):
[tex]\[
k = \frac{y}{x} = \frac{72}{48} = 1.5
\][/tex]
Through these calculations, we see that the constant of proportionality [tex]\( k \)[/tex] is [tex]\( 1.5 \)[/tex] consistently.
Now, we need to find the number of white flowers (x) needed for 90 pink flowers (y). Using the proportional relationship:
[tex]\[
y = kx \rightarrow 90 = 1.5x
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{90}{1.5} = 60
\][/tex]
Thus, the ordered pair that completes the sequence so Molly knows how many white flowers she needs for 5 rows, making the complete ordered pair [tex]\((60, 90)\)[/tex].
So, the next ordered pair is:
[tex]\((60, 90)\)[/tex]
