Questions: Rachael has a job assembling a certain car accessory. Last month she made a total of 424 items. Calculate her gross pay (in ) if she is paid on the following differential piecework schedule. Pay Level Items produced Rate per Item 1 1-160 9.18 2 Over 160 11.21

Rachael has a job assembling a certain car accessory. Last month she made a total of 424 items. Calculate her gross pay (in ) if she is paid on the following differential piecework schedule. Pay Level Items produced Rate per Item 1 1-160 9.18 2 Over 160 11.21
Transcript text: Rachael has a job assembling a certain car accessory. Last month she made a total of 424 items. Calculate her gross pay (in $\$$ ) if she is paid on the following differential piecework schedule. \begin{tabular}{|c|c|c|} \hline Pay Level & Items produced & Rate per Item \\ \hline 1 & $1-160$ & $\$ 9.18$ \\ \hline 2 & Over 160 & $\$ 11.21$ \\ \hline \end{tabular} \$
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Solution

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Solution Steps

Step 1: Calculate Pay for the First 160 Items

Rachael is paid at a rate of \(\$9.18\) per item for the first 160 items. Therefore, the pay for these items is calculated as follows:

\[ \text{Pay for first 160 items} = 160 \times 9.18 = 1468.8 \]

Step 2: Calculate Pay for Items Over 160

Rachael produced a total of 424 items. The number of items over 160 is:

\[ \text{Items over 160} = 424 - 160 = 264 \]

For these additional 264 items, she is paid at a rate of \(\$11.21\) per item. Therefore, the pay for these items is:

\[ \text{Pay for items over 160} = 264 \times 11.21 = 2959.44 \]

Step 3: Calculate Total Gross Pay

The total gross pay is the sum of the pay for the first 160 items and the pay for the items over 160:

\[ \text{Total Gross Pay} = 1468.8 + 2959.44 = 4428.24 \]

Final Answer

Rachael's gross pay for producing 424 items is \(\boxed{4428.24}\).

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