To determine the equation that represents Amy's pay when her sister's pay is [tex]$13, let's analyze the given data step by step.
### Given Data:
From the table,
- Amy's pay (in dollars): 10, 20, 30, 40
- Sister's pay (in dollars): 2, 4, 6, 8
### Step-by-Step Solution:
1. Identify Relationship between Amy's Pay and Her Sister's Pay:
We observe that Amy's pay increases as her sister's pay increases:
- When Amy's pay is 10, her sister's pay is 2.
- When Amy's pay is 20, her sister's pay is 4.
- When Amy's pay is 30, her sister's pay is 6.
- When Amy's pay is 40, her sister's pay is 8.
2. Finding the Ratio:
If we examine the ratio systematically:
- For Amy's pay of 10 and sister's pay of 2, the ratio is \(\frac{10}{2} = 5\).
- For Amy's pay of 20 and sister's pay of 4, the ratio is \(\frac{20}{4} = 5\).
- For Amy's pay of 30 and sister's pay of 6, the ratio is \(\frac{30}{6} = 5\).
- For Amy's pay of 40 and sister's pay of 8, the ratio is \(\frac{40}{8} = 5\).
Thus, \(\frac{\text{Amy's Pay}}{\text{Sister's Pay}} = 5\).
3. Expressing the Relationship as an Equation:
We can generalize this relationship as:
\[
\text{Amy's Pay} = 5 \times \text{Sister's Pay}
\]
4. Given Sister's Pay of $[/tex]13:
We are asked to find Amy's pay when her sister's pay is [tex]$13. Let's denote Amy's pay by \(x\). According to the relationship:
\[
x = 5 \times 13
\]
\[
x = 65
\]
5. Considering the Question Choices:
Let's match this relationship to the given choices:
- (A): \(y = \frac{13}{5}\)
- (B): \(5y = 13\)
- (C): \(13 = \frac{x}{5}\)
- (D): \(13 = 5x\)
6. Checking for Correct Answer:
Substituting \(x = 65\) into each option:
- (A): \(y = \frac{13}{5}\) does not make sense for this context.
- (B): \(5y = 13\) does not match since we are solving for \(x\) and it contradicts our pay rate ratio.
- (C): \(13 = \frac{x}{5}\) can be tested if we solve for \(x\):
\[
13 \times 5 = x \Rightarrow x = 65
\]
- (D): \(13 = 5x\) does not follow since it would suggest \(5x < 65\).
Hence, the correct equation representing Amy's pay when her sister's pay is $[/tex]13 is:
[tex]\[
13 = \frac{x}{5}
\][/tex]
Therefore, the answer is:
[tex]\[
(C) \ 13 = \frac{x}{5}
\][/tex]
