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Molly's garden has a unit rate of
[tex]\[ \frac{3 \text{ pink flowers}}{2 \text{ white flowers}} \][/tex]

She made a table to show how many pink and white flowers she has to plant in various rows.

\begin{tabular}{|l|c|c|c|c|}
\hline
White [tex]$(x)$[/tex] & 12 & 36 & B & C \\
\hline
Pink [tex]$(y)$[/tex] & 18 & A & 72 & 126 \\
\hline
\end{tabular}

What are the missing numbers in the table?

A: [tex]$\square$[/tex] \\
B: [tex]$\square$[/tex] \\
C: [tex]$\square$[/tex]

Sagot :

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]