To find the missing numbers in Molly's garden table, we need to utilize the given unit rate of [tex]\(\frac{3 \text{ pink flowers}}{2 \text{ white flowers}}\)[/tex]. This implies that for every 3 pink flowers, there are 2 white flowers. Mathematically, this can be expressed as the ratio [tex]\(\frac{y}{x} = \frac{3}{2}\)[/tex], where [tex]\(y\)[/tex] represents the number of pink flowers, and [tex]\(x\)[/tex] represents the number of white flowers.
Let's determine the missing values step-by-step.
### Given values in the table:
[tex]\[
\begin{array}{|l|c|c|c|c|}
\hline \text{White (}x\text{)} & 12 & 36 & B & C \\
\hline \text{Pink (}y\text{)} & 18 & A & 72 & 126 \\
\hline
\end{array}
\][/tex]
### Step 1: Calculate A
A corresponds to the number of pink flowers when the number of white flowers is 36.
Given: [tex]\(x = 36\)[/tex] (white flowers)
Using the unit rate [tex]\(\frac{y}{x} = \frac{3}{2}\)[/tex]:
[tex]\[
\frac{y}{36} = \frac{3}{2}
\][/tex]
Solving for [tex]\(y\)[/tex]:
[tex]\[
y = 36 \times \frac{3}{2} = 36 \times 1.5 = 54
\][/tex]
So, [tex]\(A = 54\)[/tex].
### Step 2: Calculate B
B corresponds to the number of white flowers when the number of pink flowers is 72.
Given: [tex]\(y = 72\)[/tex] (pink flowers)
Using the unit rate [tex]\(\frac{y}{x} = \frac{3}{2}\)[/tex]:
[tex]\[
\frac{72}{x} = \frac{3}{2}
\][/tex]
Solving for [tex]\(x\)[/tex]:
[tex]\[
x = 72 \div \frac{3}{2} = 72 \times \frac{2}{3} = 72 \times 0.6667 = 48
\][/tex]
So, [tex]\(B = 48\)[/tex].
### Step 3: Calculate C
C corresponds to the number of white flowers when the number of pink flowers is 126.
Given: [tex]\(y = 126\)[/tex] (pink flowers)
Using the unit rate [tex]\(\frac{y}{x} = \frac{3}{2}\)[/tex]:
[tex]\[
\frac{126}{x} = \frac{3}{2}
\][/tex]
Solving for [tex]\(x\)[/tex]:
[tex]\[
x = 126 \div \frac{3}{2} = 126 \times \frac{2}{3} = 126 \times 0.6667 = 84
\][/tex]
So, [tex]\(C = 84\)[/tex].
### Final Table
Now, we can fill in the missing values in the table:
[tex]\[
\begin{array}{|l|c|c|c|c|}
\hline \text{White (}x\text{)} & 12 & 36 & 48 & 84 \\
\hline \text{Pink (}y\text{)} & 18 & 54 & 72 & 126 \\
\hline
\end{array}
\][/tex]
Therefore, the missing numbers in the table are:
- [tex]\(A = 54\)[/tex]
- [tex]\(B = 48\)[/tex]
- [tex]\(C = 84\)[/tex]
