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Cindy worked for 15 consecutive days, earning an average wage of $91 per day. During the first 7 days her average was $87/day, and her average during the last 7 days was $93/day. What was her wage on the 8th day?

A. $83 B. $92 C. $97 D. $105

(I believe it's D. But feel free to correct me if i'm wrong)

User Abdul Khan
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1 Answer

2 votes

Answer:

D. $105

Explanation:

Use definition:


\text{Average of }n\text{ numbers}=\frac{\text{The sum of }n\text{ numbers}}{n}

The average wage for 15 consecutive days is $91, then by definition


\$91=\frac{\text{The sum of wages for 15 days}}{15}\Rightarrow \\ \\\text{The sum of wages for 15 days}=\$91\cdot 15=\$1,365

The average wage for first 7 consecutive days is $87, then by definition


\$87=\frac{\text{The sum of wages for first 7 days}}{7}\Rightarrow \\ \\\text{The sum of wages for first 7 days}=\$87\cdot 7=\$609

The average wage for last 7 consecutive days is $93, then by definition


\$93=\frac{\text{The sum of wages for last 7 days}}{7}\Rightarrow \\ \\\text{The sum of wages for last 7 days}=\$93\cdot 7=\$651

Now,


\text{The sum of wages for 15 days}=\text{The sum of wages for first 7 days }+\\ \\+\text{ The wage for 8th day}+\text{The sum of wages for last 7 days}\\ \\\$1,365=\$609+\text{ The wage for 8th day}+\$651\\ \\\text{ The wage for 8th day}=\$1,365-\$609-\$651=\$105

User Jan Koch
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